STANDARD DEVIATION CALCULATOR CODE

Friday, 2 October 2015

STANDARD DEVIATION CALCULATOR CODE

-----------------------------------------------------------------------------------------------------------------
COPY AND PASTE BELOW CODE IN POST HTML SECTION
-----------------------------------------------------------------------------------------------------------------

<html>
<head>
<style type="text/css">
.CalcTable {
padding: 4px 6px;
border: solid #ddd 1px;
border-collapse: collapse
}
.CalcTitleCell {
background-color: transparent;
color: #1d487e;
font-family: Verdana, Arial, sans-serif;
font-size: 130%;
font-weight: bold;
text-align: center;
height: 30px
}
.CalcInstructCell {
padding: 5px;
border-bottom: solid #ddd 1px
}
.CalcRowTitleCell {
background-color: #ccc;
color: #1d487e;
font-family: Verdana, Arial, sans-serif;
font-size: 85%;
font-weight: bold;
text-align: left;
border: solid #ddd 1px
}
.CalcColCell {
background-color: #1d487e;
color: #fff;
font-family: Verdana, Arial, sans-serif;
font-size: 100%;
font-weight: bold;
text-align: center;
border: solid #ddd 1px
}
.CalcColCellLeft {
background-color: #1d487e;
color: #fff;
font-family: Verdana, Arial, sans-serif;
font-size: 100%;
font-weight: bold;
text-align: left;
padding-left: 5px;
border: solid #ddd 1px
}
.CalcColCellRight {
background-color: #1d487e;
color: #fff;
font-family: Verdana, Arial, sans-serif;
font-size: 100%;
font-weight: bold;
text-align: right;
border: solid #ddd 1px
}
.CalcRowOdd {
background-color: #eee
}
.CalcRowEven {
background-color: #fff
}
.CalcInDescCell {
padding-left: 5px;
padding-right: 5px
}
.CalcOutDescCell {
text-align: left
}
.CalcInFldCell {
text-align: right;
padding-right: 5px;
font-size: 8pt
}
.CalcOutFldCell {
text-align: right;
padding-right: 5px;
border-left: solid #ddd 1px;
border-right: solid #ddd 1px;
font-size: 8pt
}
.CalcInFld {
font-size: 8pt
}
.CalcInFldFix {
font-size: 8pt
}
.CalcSelectFix {
font-size: 8pt
}
.CalcOutFldOddFix {
border: medium none;
background-color: #eee;
font-weight: normal;
text-align: right;
font-size: 8pt
}
.CalcOutFldEvenFix {
border: medium none;
background-color: #fff;
font-weight: normal;
text-align: right;
font-size: 8pt
}
.CalcOutFldOdd {
border: medium none;
background-color: #eee;
font-weight: normal;
text-align: right;
font-size: 8pt
}
.CalcOutFldEven {
border: medium none;
background-color: #fff;
font-weight: normal;
text-align: right;
font-size: 8pt
}
.CalcOutFldBoldOdd {
border: medium none;
background-color: #eee;
font-weight: bold;
text-align: right;
font-size: 8pt
}
.CalcOutFldBoldEven {
border: medium none;
background-color: #fff;
font-weight: bold;
text-align: right;
font-size: 8pt
}
.CalcButtonCell {
text-align: center;
border: solid #ddd 1px
}
.CalcButton {}.CalcSummaryCell {
padding-left: 5px;
padding-right: 5px;
background-color: #fff;
border: solid #ddd 1px
}
.ChartTable {
border-collapse: collapse
}
.ChartBody {}.ChartColHead1 {
background-color: #1d487e;
color: #fff;
font-family: Verdana, Arial, sans-serif;
font-size: 100%;
font-weight: bold;
text-align: center;
border: solid #ccc 1px
}
.ChartColHead1Small {
background-color: #1d487e;
color: #fff;
font-family: Arial, sans-serif;
font-size: 80%;
font-weight: bold;
text-align: center;
border: solid #ccc 1px
}
.ChartColHead2 {
background-color: #ccc;
color: #1d487e;
font-family: Verdana, Arial, sans-serif;
font-size: 85%;
font-weight: bold;
text-align: center;
border: solid #ddd 1px
}
.ChartRowOdd {
background-color: #eee
}
.ChartRowEven {
background-color: #fff
}
.ChartTextCell {
text-align: center;
padding-left: 2px;
padding-right: 2px;
border: solid #ddd 1px
}
.ChartTextCellLeft {
text-align: left;
padding-left: 2px;
padding-right: 2px;
border: solid #ddd 1px
}
.ChartNumCell {
text-align: right;
padding-left: 2px;
padding-right: 2px;
border: solid #ddd 1px
}
.ChartNumCellSmall {
font-family: Arial, sans-serif;
font-size: 85%;
text-align: right;
padding-left: 2px;
padding-right: 2px;
border: solid #ddd 1px
}
.ChartSubCell {
text-align: right;
border-top: solid #000 2px;
border-left: solid #ddd 1px;
border-right: solid #ddd 1px;
font-weight: bold;
background-color: #ccc;
padding-left: 4px;
padding-right: 2px
}
.ChartTotCell {
text-align: right;
border-top: double #000 3px;
border-bottom: double #000 3px;
border-left: solid #ddd 1px;
border-right: solid #ddd 1px;
font-weight: bold;
background-color: #ccc;
padding-left: 4px;
padding-right: 2px
}
#dhtmltooltip {
position: absolute;
left: -300px;
width: 150px;
border: 1px solid #000;
padding: 2px;
background-color: #ffffe0;
visibility: hidden;
z-index: 100;
filter: progid: DXImageTransform.Microsoft.Shadow(color=gray, direction=135)
}
#dhtmlpointer {
position: absolute;
left: -300px;
z-index: 101;
visibility: hidden
}
.div_help {
font-family: arial, verdana, helvetica, sans-serif;
font-size: small;
text-align: left;
padding: 10px
}
.SideCalcTitleCell {
font-size: 100%;
background-color: #000;
font-weight: bold;
color: #fff
}
.SideCalcResult {
text-align: right;
width: 94%;
background-color: #eee;
border: solid #000 1px;
font-family: arial, sans-serif;
font-size: 11pt;
color: #000;
padding-right: 5px
}
.SideCalcNum {
font-weight: bold;
width: 30px
}
.SideCalcSign {
font-weight: bold;
color: #00f;
width: 30px
}
.SideCalcClr {
font-weight: bold;
width: 30px;
color: red
}
.SideCalcClrTape {
font-weight: bold;
width: 94%;
color: #000
}
.SideCalcTapeCell {
text-align: center;
background-color: #ccc;
border-top: solid #ccc 1px;
border-left: solid #ccc 1px;
border-right: solid #ccc 1px;
border-bottom: dashed #000 1px;
font-family: courier, arial, sans-serif;
font-size: 10pt;
color: #000;
padding-right: 0px;
padding-left: 0px
}
.BelowCalcTable {
border-collapse: collapse
}
.BelowCalcAdCell {}.BelowCalcColHead {
background-color: #ccc;
color: #1d487e;
font-family: Verdana, Arial, sans-serif;
font-size: 85%;
font-weight: bold;
text-align: center;
border: solid #ccc 1px
}
.BelowCalcImgHead {
background-color: #ccc;
text-align: center;
border: solid #ccc 1px
}
.BelowCalcLinkCell {
text-align: left;
padding-left: 2px;
padding-right: 2px;
border: solid #ddd 1px
}
.sppTable {
width: 300px;
border-collapse: collapse
}
.sppRow {
background-color: #ddd
}
.sppColHead {
background-color: #fff;
color: #1d487e;
font-family: Verdana, Arial, sans-serif;
font-size: 85%;
font-weight: bold;
text-align: center;
width: 240px;
border-left: solid #8f8fb3 1px;
border-top: solid #8f8fb3 1px
}
.sppImgHead {
background-color: #fff;
text-align: center;
width: 60px;
border-right: solid #8f8fb3 1px;
border-top: solid #8f8fb3 1px
}
.sppLinkCell {
font-size: 85%;
text-align: left;
padding-left: 2px;
padding-right: 2px;
border-left: solid #8f8fb3 1px;
border-bottom: solid #8f8fb3 1px;
border-right: solid #8f8fb3 1px
}
.fb_like_button {
border: 1px dotted #000;
background-color: #eee;
padding: 10px;
width: 320px;
float: right
}
.blogItItem {
margin: 18px 0;
padding: 0 12px;
border: 1px solid #ccc;
background: #eee;
box-shadow: 4px 4px 4px #ccc
}
.blogItItem h6 {
font-style: normal;
font-weight: normal;
font-size: 80%
}
.leftnav_heading {
text-align: center
}
.leftnav_heading a {
font-family: Arial, Helvetica, sans-serif;
font-size: 15px;
text-align: left;
line-height: 14px;
background-image: url();
color: #333;
text-decoration: none;
width: 169px;
height: 41px;
display: block;
font-weight: bold;
margin-top: 18px
}
.leftnav_heading a:hover {
background-image: url()
}
.leftnav_heading span {
display: block;
padding: 7px
}
.texttop {
font-size: 15px;
line-height: 14px;
color: #333;
text-shadow: 0px 0px 2px #fff;
margin-bottom: 10px
}
.textbottom {
color: #333;
font-size: 15px;
text-shadow: 0px 0px 2px #fff
}
#mobileBtnDiv {
display: none
}
@media only screen and (max-device-width: 640px) {
#mobileBtnDiv {
display: block;
width: 100%;
text-align: center;
padding: 10px
}
#mobileBtn {
display: inline-block;
text-align: center;
width: 50%;
font-size: 2em;
line-height: 2em;
background-color: #0f5378;
color: #fff;
text-decoration: none;
border-radius: 10px;
border: 1px solid #fff
}
#mobileBtn:hover {
background-color: #4cc2ce;
color: #087197
}
}
</style>

<script>
var mod_pagespeed_OadpizgvRP = "var result_ar=new Array();function customSort(a,b){return(b-a)*-1;}\nfunction decChk(n){var mod=n%1;if(mod!=0){return fns(n,2,0,0,0);}else{return n;}}\nfunction calc_stats(form){var v_nums=document.calc.nums.value;if(v_nums.length==0){alert(\"Please enter a set of numbers to calculate the statistics for.\");document.calc.nums.focus();}else{var fnl_num_ar=new Array();var num_val=0;var accum_num=0;if(v_nums.indexOf(\"\\r\")>-1){while(v_nums.indexOf(\"\\r\")>-1){v_nums=v_nums.replace(\"\\r\",\" \");}}\nif(v_nums.indexOf(\"\\n\")>-1){while(v_nums.indexOf(\"\\n\")>-1){v_nums=v_nums.replace(\"\\n\",\" \");}}\nif(v_nums.indexOf(\",\")>-1){var num_ar=v_nums.split(\",\");}else{var num_ar=v_nums.split(\" \");}\nfor(var i=0;i<num_ar.length;i++){if(num_ar[i]!=\" \"&&num_ar[i]!=\"\"){if(num_ar[i].indexOf(\"x\")>-1){var set_ar=num_ar[i].split(\"x\");mult=Number(set_ar[1]);num_val=Number(set_ar[0]);for(var j=0;j<mult;j++){fnl_num_ar.push(num_val);accum_num+=Number(num_val);}}else{num_val=sn(num_ar[i]);accum_num+=Number(num_val);fnl_num_ar.push(num_val);}}}\nvar v_num_nums=fnl_num_ar.length;document.calc.num_nums.value=v_num_nums;var v_num_sum=accum_num;document.calc.num_sum.value=v_num_sum;var v_avg=accum_num/v_num_nums;document.calc.avg.value=v_avg;var tbl=\"<center><table class='ChartTable' width='90%' style='font-family: serif;'>\";tbl+=\"<tr>\";tbl+=\"<th width='15%' class='ChartColHead2'>Count n</th>\";tbl+=\"<th width='15%' class='ChartColHead2'>X</th>\";tbl+=\"<th width='35%' class='ChartColHead2'>X - μ</th>\";tbl+=\"<th width='35%' class='ChartColHead2'>(X - μ)2</th>\";tbl+=\"</tr>\";var avgX=0;var avgX2=0;var accum_avgX2=0;for(var x=0;x<fnl_num_ar.length;x++){avgX=fnl_num_ar[x]-v_avg;avgX2=avgX*avgX;if(x%2==0){tbl+=\"<tr class='ChartRowEven'>\";}else{tbl+=\"<tr class='ChartRowOdd'>\";}\ntbl+=\"<td width='15%' class='ChartNumCell'>\"+(x+1)+\"</td>\";tbl+=\"<td width='15%' class='ChartNumCell'>\"+fnl_num_ar[x]+\"</td>\";tbl+=\"<td width='35%' class='ChartNumCell'>\"+fnl_num_ar[x]+\" - \"+decChk(v_avg)+\" = \"+decChk(avgX)+\"</td>\";tbl+=\"<td width='35%' class='ChartNumCell'>(\"+decChk(avgX)+\")2 = \"+decChk(avgX2)+\"</td>\";tbl+=\"</tr>\";accum_avgX2+=avgX2;}\ntbl+=\"<tr>\";tbl+=\"<td width='15%' class='ChartTotCell'>n = \"+v_num_nums+\"</td>\";tbl+=\"<td width='15%' class='ChartTotCell'>Sum = \"+v_num_sum+\"</td>\";tbl+=\"<td width='35%' class='ChartTotCell'> </td>\";tbl+=\"<td width='35%' class='ChartTotCell'>Σ (X - μ)2 = \"+decChk(accum_avgX2)+\"</td>\";tbl+=\"</tr>\";tbl+=\"</table></center>\";var v_pop_var=accum_avgX2/v_num_nums;document.calc.pop_var.value=v_pop_var;v_std_dev=Math.sqrt(v_pop_var);document.calc.std_dev.value=v_std_dev;var v_samp_var=accum_avgX2/(v_num_nums-1);document.calc.samp_var.value=v_samp_var;v_std_dev_sample=Math.sqrt(v_samp_var);document.calc.std_dev_sample.value=v_std_dev_sample;var v_summary=\" <img src='https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHSLSkgqRY3PY_iFXdVxZzoPMK12-GxS8IPLF3nONJTGil5Q6QndcuvQRCPGPByHYCMcgl3VSzfR0qAkMJvnpaz6V-xzGJNDWC00aZY3aPNIIPzoesvPpp_qVyIrdLbs69xt8kNPaco3ZR/s72-c/BASIC+JAVA+CALCULATOR.png' width='60' height='54' class='ItemLeft' />\";v_summary+=\"(Decimals in this section have been rounded to 2 places)\";v_summary+=\"According to my calculations, the Population Standard Deviation of the entered number set \";v_summary+=\"is \"+decChk(v_std_dev)+\". Or, if the data set you entered \";v_summary+=\"represents only a sampling of the population set, then in that case the Sample \";v_summary+=\"Standard Deviation would be \";v_summary+=\"\"+decChk(v_std_dev_sample)+\". Here are the steps I took to \";v_summary+=\"arrive at the results:\";v_summary+=\"Step #1: Find the mean of data set: To find the mean of the data \";v_summary+=\"set we simply total all of the values in the set and then divide by how many \";v_summary+=\"items are in the set, like this:\";v_summary+=\"<center><table>\";v_summary+=\"<tr>\";v_summary+=\"<td rowspan='2' style='text-align:center; vertical-align: middle'>Mean of set (μ) = </td>\";v_summary+=\"<td style='text-align:center;'>\"+v_num_sum+\"</td>\";v_summary+=\"<td rowspan='2' style='text-align:center; vertical-align: middle'> = \"+decChk(v_avg)+\"</td>\";v_summary+=\"</tr>\";v_summary+=\"<tr>\";v_summary+=\"<td style='text-align:center; border-top: 1px solid #000'>\"+v_num_nums+\"</td>\";v_summary+=\"</tr>\";v_summary+=\"</table></center>\";v_summary+=\"Step #2: Find the sum of the squared distances from the mean. \";v_summary+=\"For each item in the data set we: (1) subtract the mean of the entire set \";v_summary+=\"from the item, (2) square the \";v_summary+=\"result, and then (3) sum all of the squared results, like this:\"+tbl+\" \";v_summary+=\"Step #3: Calculate the variance. This step depends on whether or \";v_summary+=\"not the set you are working with represents the total data (population) or partial \";v_summary+=\"data (sample). Here is how you calculate the variance from the results in step #2 \";v_summary+=\"for either case (μ and X are both symbols for Mean, with the only real difference indicated by red text):\";v_summary+=\"<center><table width='90%' style='font-family: serif;'>\";v_summary+=\"<tr>\";v_summary+=\"<td colspan='5' class='ChartColHead2'>Population Variance (σ2)</td>\";v_summary+=\"</tr>\";v_summary+=\"<tr>\";v_summary+=\"<td width='10%' rowspan='2' style='text-align:center; vertical-align: middle'>σ2 = </td>\";v_summary+=\"<td width='25%' style='text-align:center;'>Σ (X - μ)2</td>\";v_summary+=\"<td width='5%' rowspan='2' style='text-align:center; vertical-align: middle'> = </td>\";v_summary+=\"<td width='15%' style='text-align:center; vertical-align: bottom;'>\"+decChk(accum_avgX2)+\"</td>\";v_summary+=\"<td width='45%' rowspan='2' style='text-align:left; vertical-align: middle'> = \"+decChk(v_pop_var)+\"</td>\";v_summary+=\"</tr>\";v_summary+=\"<tr>\";v_summary+=\"<td style='text-align:center; border-top: 1px solid #000; color: red;'>n</td>\";v_summary+=\"<td style='text-align:center; border-top: 1px solid #000'>\"+v_num_nums+\"</td>\";v_summary+=\"</tr>\";v_summary+=\"</table></center> \";v_summary+=\"<center><table width='90%' style='font-family: serif;'>\";v_summary+=\"<tr>\";v_summary+=\"<td colspan='5' class='ChartColHead2'>Sample Variance (s2)</td>\";v_summary+=\"</tr>\";v_summary+=\"<tr>\";v_summary+=\"<td width='10%' rowspan='2' style='text-align:center; vertical-align: middle'>s2 = </td>\";v_summary+=\"<td width='25%' style='text-align:center;'>Σ (X - X)2</td>\";v_summary+=\"<td width='5%' rowspan='2' style='text-align:center; vertical-align: middle'> = </td>\";v_summary+=\"<td width='15%' style='text-align:center; vertical-align: bottom;'>\"+decChk(accum_avgX2)+\"</td>\";v_summary+=\"<td width='45%' rowspan='2' style='text-align:left; vertical-align: middle'> = \"+decChk(v_samp_var)+\"</td>\";v_summary+=\"</tr>\";v_summary+=\"<tr>\";v_summary+=\"<td style='text-align:center; border-top: 1px solid #000; color: red;'>n - 1</td>\";v_summary+=\"<td style='text-align:center; border-top: 1px solid #000'>\"+(v_num_nums-1)+\"</td>\";v_summary+=\"</tr>\";v_summary+=\"</table></center>\";v_summary+=\"Step #4: Calculate the square root of the variance. This step is \";v_summary+=\"basically the same for both the population and the sample standard deviation calculations. \";v_summary+=\"The only difference is that the Variance was computed differently in Step #3 (n in denominator vs n - 1):\";v_summary+=\"<center><table width='90%' style='font-family: serif;'>\";v_summary+=\"<tr>\";v_summary+=\"<td colspan='5' class='ChartColHead2'>Population Standard Deviation (σ)</td>\";v_summary+=\"</tr>\";v_summary+=\"<tr>\";v_summary+=\"<td width='25%' style='text-align:right; vertical-align: middle;'>σ = √</td>\";v_summary+=\"<td width='10%' style='text-align:left; border-top: 1px solid black'>σ2</td>\";v_summary+=\"<td width='5%' style='text-align:right;'> = √</td>\";v_summary+=\"<td width='30%' style='text-align:center; border-top: 1px solid black'>\"+decChk(v_pop_var)+\"</td>\";v_summary+=\"<td width='30%' style='text-align:left;'> = \"+decChk(v_std_dev)+\"</td>\";v_summary+=\"</tr>\";v_summary+=\"</table></center> \";v_summary+=\"<center><table width='90%' style='font-family: serif;'>\";v_summary+=\"<tr>\";v_summary+=\"<td colspan='5' class='ChartColHead2'>Sample Standard Deviation (s)</td>\";v_summary+=\"</tr>\";v_summary+=\"<tr>\";v_summary+=\"<td width='25%' style='text-align:right; vertical-align: middle;'>s = √</td>\";v_summary+=\"<td width='10%' style='text-align:left; border-top: 1px solid black'>s2</td>\";v_summary+=\"<td width='5%' style='text-align:right;'> = √</td>\";v_summary+=\"<td width='30%' style='text-align:center; border-top: 1px solid black'>\"+decChk(v_samp_var)+\"</td>\";v_summary+=\"<td width='30%' style='text-align:left;'> = \"+decChk(v_std_dev_sample)+\"</td>\";v_summary+=\"</tr>\";v_summary+=\"</table></center>\";document.getElementById(\"summary\").innerHTML=v_summary+\" \";}}\nfunction delim_set(form){var delim_ar=[\", \",\",\",\" \",\"\\r\",\"\\t\"];var new_delim_idx=document.calc.r_delim.selectedIndex;var new_delim=delim_ar[new_delim_idx];var new_str=\"\";for(var i=0;i<result_ar.length;i++){if(i==0){new_str+=\"\"+result_ar[i]+\"\";}else{new_str+=new_delim+\"\"+result_ar[i]+\"\";}}\ndocument.calc.r_set.value=new_str;}\nfunction clear_results(form){document.calc.num_nums.value=\"\";document.calc.num_sum.value=\"\";document.calc.avg.value=\"\";document.calc.pop_var.value=\"\";document.calc.std_dev.value=\"\";document.calc.samp_var.value=\"\";document.calc.std_dev_sample.value=\"\";document.getElementById(\"summary\").innerHTML=\"\";}\nfunction reset_calc(form){document.getElementById(\"summary\").innerHTML=\"\";document.calc.reset();}";
var mod_pagespeed_PJWHvBYF1j = "var offsetfromcursorX=12\nvar offsetfromcursorY=10\nvar offsetdivfrompointerX=10\nvar offsetdivfrompointerY=14\ndocument.write('<div class=\"div_help\" id=\"dhtmltooltip\" onClick=\"hideddrivetip()\"></div>')\ndocument.write('<img id=\"dhtmlpointer\" src=\"https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHSLSkgqRY3PY_iFXdVxZzoPMK12-GxS8IPLF3nONJTGil5Q6QndcuvQRCPGPByHYCMcgl3VSzfR0qAkMJvnpaz6V-xzGJNDWC00aZY3aPNIIPzoesvPpp_qVyIrdLbs69xt8kNPaco3ZR/s72-c/BASIC+JAVA+CALCULATOR.png\">')\nvar ie=document.all\nvar ns6=document.getElementById&&!document.all\nvar enabletip=false\nif(ie||ns6)\nvar tipobj=document.all?document.all[\"dhtmltooltip\"]:document.getElementById?document.getElementById(\"dhtmltooltip\"):\"\"\nvar pointerobj=document.all?document.all[\"dhtmlpointer\"]:document.getElementById?document.getElementById(\"dhtmlpointer\"):\"\"\nfunction ietruebody(){return(document.compatMode&&document.compatMode!=\"BackCompat\")?document.documentElement:document.body}\nfunction ddrivetip(thetext,thewidth,thecolor){if(ns6||ie){if(typeof thewidth!=\"undefined\")tipobj.style.width=thewidth+\"px\"\nif(typeof thecolor!=\"undefined\"&&thecolor!=\"\")tipobj.style.backgroundColor=thecolor\ntipobj.innerHTML=thetext\nenabletip=true\nreturn false}}\nfunction positiontip(e){if(enabletip){var nondefaultpos=false\nvar curX=(ns6)?e.pageX:event.clientX+ietruebody().scrollLeft;var curY=(ns6)?e.pageY:event.clientY+ietruebody().scrollTop;var winwidth=ie&&!window.opera?ietruebody().clientWidth:window.innerWidth-20\nvar winheight=ie&&!window.opera?ietruebody().clientHeight:window.innerHeight-20\nvar rightedge=ie&&!window.opera?winwidth-event.clientX-offsetfromcursorX:winwidth-e.clientX-offsetfromcursorX\nvar bottomedge=ie&&!window.opera?winheight-event.clientY-offsetfromcursorY:winheight-e.clientY-offsetfromcursorY\nvar leftedge=(offsetfromcursorX<0)?offsetfromcursorX*(-1):-1000\nif(rightedge<tipobj.offsetWidth){tipobj.style.left=curX-tipobj.offsetWidth+\"px\"\nnondefaultpos=true}\nelse if(curX<leftedge)\ntipobj.style.left=\"5px\"\nelse{tipobj.style.left=curX+offsetfromcursorX-offsetdivfrompointerX+\"px\"\npointerobj.style.left=curX+offsetfromcursorX+\"px\"}\nif(bottomedge<tipobj.offsetHeight){tipobj.style.top=curY-tipobj.offsetHeight-offsetfromcursorY+\"px\"\nnondefaultpos=true}\nelse{tipobj.style.top=curY+offsetfromcursorY+offsetdivfrompointerY+\"px\"\npointerobj.style.top=curY+offsetfromcursorY+\"px\"}\ntipobj.style.visibility=\"visible\"\nif(!nondefaultpos)\npointerobj.style.visibility=\"visible\"\nelse\npointerobj.style.visibility=\"hidden\"}}\nfunction hideddrivetip(){if(ns6||ie){enabletip=false\ntipobj.style.visibility=\"hidden\"\npointerobj.style.visibility=\"hidden\"\ntipobj.style.left=\"-1000px\"\ntipobj.style.backgroundColor=''\ntipobj.style.width=''}}\ndocument.onmousemove=positiontip\nfunction sn(num){num=num.toString();var len=num.length;var rnum=\"\";var test=\"\";var j=0;var b=num.substring(0,1);if(b==\"-\"){rnum=\"-\";}\nfor(i=0;i<=len;i++){b=num.substring(i,i+1);if(b==\"0\"||b==\"1\"||b==\"2\"||b==\"3\"||b==\"4\"||b==\"5\"||b==\"6\"||b==\"7\"||b==\"8\"||b==\"9\"||b==\".\"){rnum=rnum+\"\"+b;}}\nif(rnum==\"\"||rnum==\"-\"){rnum=0;}\nrnum=Number(rnum);return rnum;}\nfunction fns(num,places,comma,type,show){var sym_1=\"$\";var sym_2=\"\";var isNeg=0;if(num<0){num=num*-1;isNeg=1;}\nvar myDecFact=1;var myPlaces=0;var myZeros=\"\";while(myPlaces<places){myDecFact=myDecFact*10;myPlaces=Number(myPlaces)+Number(1);myZeros=myZeros+\"0\";}\nonum=Math.round(num*myDecFact)/myDecFact;integer=Math.floor(onum);if(Math.ceil(onum)==integer){decimal=myZeros;}else{decimal=Math.round((onum-integer)*myDecFact)}\ndecimal=decimal.toString();if(decimal.length<places){fillZeroes=places-decimal.length;for(z=0;z<fillZeroes;z++){decimal=\"0\"+decimal;}}\nif(places>0){decimal=\".\"+decimal;}\nif(comma==1){integer=integer.toString();var tmpnum=\"\";var tmpinteger=\"\";var y=0;for(x=integer.length;x>0;x--){tmpnum=tmpnum+integer.charAt(x-1);y=y+1;if(y==3&x>1){tmpnum=tmpnum+\",\";y=0;}}\nfor(x=tmpnum.length;x>0;x--){tmpinteger=tmpinteger+tmpnum.charAt(x-1);}\nfinNum=tmpinteger+\"\"+decimal;}else{finNum=integer+\"\"+decimal;}\nif(isNeg==1){if(type==1&&show==1){finNum=\"-\"+sym_1+\"\"+finNum+\"\"+sym_2;}else{finNum=\"-\"+finNum;}}else{if(show==1){if(type==1){finNum=sym_1+\"\"+finNum+\"\"+sym_2;}else\nif(type==2){finNum=finNum+\"%\";}}}\nreturn finNum;}\nfunction side_calc_b(num){var v_result=document.side_calc.result.value;if(v_result.length<10){var v_new_result=v_result+\"\"+num;document.side_calc.result.value=v_new_result;}}\nfunction side_calc_del(num){var v_result=document.side_calc.result.value;if(v_result.length>0){var v_new_result=v_result.substring(0,v_result.length-1);document.side_calc.result.value=v_new_result;}}\nfunction side_calc_sign(sgn){document.side_calc.h_sign.value=sgn;document.side_calc.h_num_1.value=document.side_calc.result.value;document.side_calc.result.value=\"\";var tape_sgn=\"\";if(sgn!=\"\"){if(sgn==\"/\"){tape_sgn=\"÷\";}else\nif(sgn==\"*\"){tape_sgn=\"×\";}else\nif(sgn==\"-\"){tape_sgn=\"-\";}else\nif(sgn==\"+\"){tape_sgn=\"+\";}}\nvar tape_new=document.getElementById(\"side_calc_tape_new\").innerHTML;var new_tape=\"\"+document.side_calc.h_num_1.value+\" \"+tape_sgn+\"\";document.getElementById(\"side_calc_tape_new\").innerHTML=new_tape;}\nfunction side_calc_equal(form){var v_1=Number(document.side_calc.h_num_1.value);var v_2=Number(document.side_calc.result.value);var v_sign=document.getElementById(\"h_sign\").value;var v_new_result=0;if(v_sign!=\"\"){if(v_sign==\"/\"){v_new_result=v_1/v_2;}else\nif(v_sign==\"*\"){v_new_result=v_1*v_2;}else\nif(v_sign==\"-\"){v_new_result=v_1-v_2;}else\nif(v_sign==\"+\"){v_new_result=v_1+v_2;}\nif(v_new_result>99999999.99||v_new_result<-99999999.99){alert(\"Sorry, the result is too big (greater than 1 billion) for this calculator.\");}else{document.side_calc.result.value=v_new_result;document.side_calc.h_num_1.value=v_new_result;document.side_calc.h_sign.value=\"\";var tape_new=document.getElementById(\"side_calc_tape_new\").innerHTML;var new_tape=\"\"+tape_new+\" \"+v_2+\" = \"+v_new_result+\"\";document.getElementById(\"side_calc_tape_new\").innerHTML=\"\";var tape_old=document.getElementById(\"side_calc_tape_old\").innerHTML;document.getElementById(\"side_calc_tape_old\").innerHTML=\"\"+new_tape+\"<hr style='border: dashed #EEEEEE 1px; line-height: 1;'>\"+tape_old+\"\";document.getElementById(\"side_calc_tape_but\").innerHTML=\"<input type='button' value='Throw Away' onClick='side_calc_clr_tape(this.form)' class='SideCalcClrTape' />\";}}}\nfunction side_calc_pm(form){var v_pm=Number(document.side_calc.result.value);v_pm=v_pm*-1;document.side_calc.result.value=v_pm;}\nfunction side_calc_clr(form){document.side_calc.result.value=\"\";document.side_calc.h_num_1.value=\"\";document.side_calc.h_sign.value=\"\";}\nfunction side_calc_clr_tape(form){document.getElementById(\"side_calc_tape_new\").innerHTML=\"\";document.getElementById(\"side_calc_tape_old\").innerHTML=\"\";document.getElementById(\"side_calc_tape_but\").innerHTML=\"\";}\nvar soc_ad_ar=[[0,\"\",\"\",\"\"],[1,\"Auto\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[2,\"Budget\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[3,\"Credit\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[4,\"Debt\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[5,\"Income\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[6,\"Invest\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[7,\"Loan\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[8,\"Mortgage\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[9,\"Finance\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[10,\"Retire\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[11,\"College\",\"WyzAnt\",\"Find a <a href='http://www.shareasale.com/r.cfm?b=246096&u=724440&m=28558&urllink=&afftrack=' rel='nofollow' target='_blank'>local tutor</a> today!\"],[12,\"Business\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[13,\"\",\"\",\"\"],[14,\"\",\"\",\"\"],[15,\"\",\"\",\"\"],[16,\"\",\"\",\"\"],[17,\"\",\"\",\"\"],[18,\"\",\"\",\"\"],[19,\"\",\"\",\"\"],[20,\"Date\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[21,\"Conversion\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[22,\"Math\",\"WyzAnt\",\"Find a local <a href='http://www.shareasale.com/r.cfm?b=246097&u=724440&m=28558&urllink=&afftrack=' rel='nofollow' target='_blank'>math tutor</a> today!\"],[23,\"Date\",\"SocialMedia\",\"If you like this calculator, please pay it forward with a Like, Tweet, +1, or Pin.\"],[24,\"Sports\",\"SocialMedia\",\"If you like this web app, please pay it forward with a Like, Tweet, +1, or Pin.\"]];";
</script>

<script>eval(mod_pagespeed_OadpizgvRP);</script>
<script>eval(mod_pagespeed_PJWHvBYF1j);</script>

</head>

<body>
<form name="calc" method="post" action="#">
<table class="CalcTable">
<tbody>
<tr>
<td colspan="2" align="center" class="CalcTitleCell">
STANDARD DEVIATION CALCULATOR
</td>
</tr>
<tr>
<td colspan="2" class="CalcInstructCell">
 
 
Instructions: Enter each number in the data set separated by a comma, a space, a line return, or any combination of the three (you can also paste a set of numbers into the number field as long as they are separated by one of the mentioned delimiters).

Note that you can also enter multiples of the same number by entering the number, followed by a lower case "x", followed by the multiplier (no spaces before or after the x). For example, to enter a 3 four times, you would enter 3x4.


Once you have all of the numbers entered in the number set, click the "Calculate Standard Deviation" button.


Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the Standard Deviation Calculator.

</td>
</tr>
<tr class="ChartRowEven">
<td width="600" colspan="2" class="ChartTextCellLeft">
<img src="data:image/jpeg;base64,/9j/4AAQSkZJRgABAgAAZABkAAD/2wBDAAYEBAQFBAYFBQYJBgUGCQsIBgYICwwKCgsKCgwQDAwMDAwMEAwODxAPDgwTExQUExMcGxsbHB8fHx8fHx8fHx//2wBDAQcHBw0MDRgQEBgaFREVGh8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx//wAARCAAPAA8DAREAAhEBAxEB/8QAFQABAQAAAAAAAAAAAAAAAAAABQP/xAAkEAACAgEDBAIDAAAAAAAAAAABAgMFBAYRIQAHEjETIhUjYf/EABYBAQEBAAAAAAAAAAAAAAAAAAIDBf/EACARAQAABgIDAQAAAAAAAAAAAAEAAgMREkExURNhceH/2gAMAwEAAhEDEQA/AL5OrLB+4uo6+zvdSmBLLKhra6kyX+UkZLqEVXYqqog4AH862SkeOVCXjcZjO5os3OoYr/z+J3mXSA1ZcZ9ZNj5SMWzJWnjaSvlbY/Yx/NE+xU7cMAffU5sWjniD89wy5UxybfkDrp3VEHd+1salYcvMaysHxMbCtqyHM/Y8vlskrZDKRGW81aLcDf0eRTOVpA9Gm0DCbyKduyAtHaOu4LvId8iuLmutUAS1rZH85K3IQcJkM23k32b0o5OwBPVatUtvk09nqBTpt9cOzqP/2Q==" alt="Help" onMouseover="ddrivetip('Enter each element of the data set (or paste a copied data set) into this text box. Be sure each number is separated by a space, a comma, a line return, or any combination of the three. Also, if you wish to enter a frequency for each number, enter the number, followed by a lowercase x, followed by the multiplier (for 3 number twos, enter 2x3).', 250)" ; onMouseout="hideddrivetip()">
Enter or paste numbers in data set (separated by comma, space, or return): 
<center>
<textarea name="nums" rows="10" cols="60" wrap="virtual" onKeyUp="clear_results(this.form)"></textarea>
</center>
</td>
</tr>
<tr class="ChartRowOdd">
<td colspan="2" class="ChartTextCell">
<input type="button" class="CalcButton" value="Calculate Standard Deviation" onClick="calc_stats(this.form)"/>
<input type="button" class="CalcButton" value="Reset" onClick="reset_calc(this.form)"/>
</td>
</tr>
<tr class="ChartRowEven">
<td width="300" class="ChartTextCellLeft">
<img src="data:image/jpeg;base64,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" alt="Help" onMouseover="ddrivetip('This is the total number of items detected in the data set field.', 250)" ; onMouseout="hideddrivetip()">
Total number of items in set:
</td>
<td width="300" class="ChartTextCell">
<input type="text" id="num_nums" name="num_nums" size="25" value="" class="CalcOutFldEven"/>
</td>
</tr>
<tr class="ChartRowOdd">
<td width="300" class="ChartTextCellLeft">
<img src="data:image/jpeg;base64,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" alt="Help" onMouseover="ddrivetip('This is the sum of all items in the set.', 250)" ; onMouseout="hideddrivetip()">
Sum of items in set:
</td>
<td width="300" class="ChartTextCell">
<input type="text" id="num_sum" name="num_sum" size="25" value="" class="CalcOutFldOdd"/>
</td>
</tr>
<tr class="ChartRowEven">
<td width="300" class="ChartTextCellLeft">
<img src="data:image/jpeg;base64,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" alt="Help" onMouseover="ddrivetip('This is the average or mean of the items within the data set. This is calculated by summing the items within the set, and then dividing the sum by the number of items.', 250)" ; onMouseout="hideddrivetip()">
Mean:
</td>
<td width="300" class="ChartTextCell">
<input type="text" id="avg" name="avg" size="25" value="" class="CalcOutFldEven"/>
</td>
</tr>
<tr class="ChartRowOdd">
<td width="300" class="ChartTextCellLeft">
<img src="data:image/jpeg;base64,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" alt="Help" onMouseover="ddrivetip('This is the variance of the data set (also called the Mean of Squared Differences) if the items entered represent the entire (population) data set.', 250)" ; onMouseout="hideddrivetip()">
Population variance:
</td>
<td width="300" class="ChartTextCell">
<input type="text" id="pop_var" name="pop_var" size="25" value="" class="CalcOutFldOdd"/>
</td>
</tr>
<tr class="ChartRowEven">
<td width="300" class="ChartTextCellLeft">
<img src="data:image/jpeg;base64,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" alt="Help" onMouseover="ddrivetip('This is the population standard deviation, which is calculated by finding the square root of the population variance.', 250)" ; onMouseout="hideddrivetip()">
Population standard deviation:
</td>
<td width="300" class="ChartTextCell">
<input type="text" id="std_dev" name="std_dev" size="25" value="" class="CalcOutFldEven"/>
</td>
</tr>
<tr class="ChartRowOdd">
<td width="300" class="ChartTextCellLeft">
<img src="data:image/jpeg;base64,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" alt="Help" onMouseover="ddrivetip('This is the variance of the data set (also called the Mean of Squared Differences) if the items entered represent only a portion (sample) of the data.', 250)" ; onMouseout="hideddrivetip()">
Sample variance:
</td>
<td width="300" class="ChartTextCell">
<input type="text" id="samp_var" name="samp_var" size="25" value="" class="CalcOutFldOdd"/>
</td>
</tr>
<tr class="ChartRowEven">
<td width="300" class="ChartTextCellLeft">
<img src="data:image/jpeg;base64,/9j/4AAQSkZJRgABAgAAZABkAAD/2wBDAAYEBAQFBAYFBQYJBgUGCQsIBgYICwwKCgsKCgwQDAwMDAwMEAwODxAPDgwTExQUExMcGxsbHB8fHx8fHx8fHx//2wBDAQcHBw0MDRgQEBgaFREVGh8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx//wAARCAAPAA8DAREAAhEBAxEB/8QAFQABAQAAAAAAAAAAAAAAAAAABQP/xAAkEAACAgEDBAIDAAAAAAAAAAABAgMFBAYRIQAHEjETIhUjYf/EABYBAQEBAAAAAAAAAAAAAAAAAAIDBf/EACARAQAABgIDAQAAAAAAAAAAAAEAAgMREkExURNhceH/2gAMAwEAAhEDEQA/AL5OrLB+4uo6+zvdSmBLLKhra6kyX+UkZLqEVXYqqog4AH862SkeOVCXjcZjO5os3OoYr/z+J3mXSA1ZcZ9ZNj5SMWzJWnjaSvlbY/Yx/NE+xU7cMAffU5sWjniD89wy5UxybfkDrp3VEHd+1salYcvMaysHxMbCtqyHM/Y8vlskrZDKRGW81aLcDf0eRTOVpA9Gm0DCbyKduyAtHaOu4LvId8iuLmutUAS1rZH85K3IQcJkM23k32b0o5OwBPVatUtvk09nqBTpt9cOzqP/2Q==" alt="Help" onMouseover="ddrivetip('This is the sample standard deviation, which is calculated by finding the square root of the sample variance.', 250)" ; onMouseout="hideddrivetip()">
Sample standard deviation:
</td>
<td width="300" class="ChartTextCell">
<input type="text" id="std_dev_sample" name="std_dev_sample" size="25" value="" class="CalcOutFldEven"/>
</td>
</tr>
<tr class="ChartRowOdd">
<td width="600" colspan="2" class="CalcSummaryCell" id="summary">
</td>
</tr>
</tbody>
</table>
</form>
</body>
</html>

Don't Let the Formula Scare You!

In my opinion, if the "powers that be" really wanted to entice kids into embracing mathematics, they would use kittens, puppies, bunny rabbits, etc., as math symbols, not Greek (geek) letters.

Want to scare a math-challenged student into closing the math textbook so fast that it blows out the candles in the room? Show them this:

σ² =

_N	(X_i - μ)²
Σ
ⁱ⁼¹

σ = √

σ²

That's the scary-looking formula for calculating the variance (σ²) and standard deviation (σ) of a population data set.

But wait! Keep your candles burning!

As you will see in the example further down the page, the steps to calculating variance and standard deviation are much easier than trying to decipher the Greek/geek formula.

What is Standard Deviation?

Standard Deviation is simply one of several methods for summarizing the dispersion of the values in a set of data.

Specifically, standard deviation is the square root of the variance, which attempts to summarize the variability or dispersion of values relative to the mean of the entire set.

A small standard deviation indicates the values are tightly grouped around the mean (average) of the data set.

A large standard deviation indicates the values are not tightly grouped around the mean (average) of the data set.

Population Vs Sample Statistics

Population: The data set is the total set of elements of interest for a given problem. Population parameters in the formulas on this page are denoted by σ and μ.

Sample: The data set represents only a fraction of the population as defined above. Sample parameters in the formulas on this page are denoted by s and X.

4 Simple Steps

As I stated earlier, calculating standard deviation is much easier than the formula depicts. Here are the 4 simple steps:

Find the mean of the data set.

Find the sum of the squared differences from the mean.

Divide the result in step #2 by n (population) or n - 1 (sample), where n is the number of items in the set.

Find the square root of the result in step #3.

To see just how easy the above steps are, let me walk you through an example.

Example Problem

To illustrate how easy it is to calculate variance and standard deviation, I will use the following data set:

5, 4, 7, 9, 6, 8, 7, 5, 4, 5

Note: Decimals in this example are rounded to 2 places before they are displayed on the screen.

Step #1: Calculate the mean

The mean is the average of all numbers in a data set. To calculate the mean of set of numbers, you add all of the items together and then divide that result by the number of items within the set.

Data set: 5, 4, 7, 9, 6, 8, 7, 5, 4, 5

Data set contains 10 items

Mean = (5 + 4 + 7 + 9 + 6 + 8 + 7 + 5 + 4) ÷ 10

Mean = 60 ÷ 10

Mean = 6

Step #2: Find the sum of the squared distances from the mean.

For each item in the data set we: (1) subtract the mean of the entire set from the item, (2) square the result, and then (3) sum all of the squared results, like this:

Count n	X	X - μ	(X - μ)²
1	5	5 - 6 = -1	(-1)² = 1
2	4	4 - 6 = -2	(-2)² = 4
3	7	7 - 6 = 1	(1)² = 1
4	9	9 - 6 = 3	(3)² = 9
5	6	6 - 6 = 0	(0)² = 0
6	8	8 - 6 = 2	(2)² = 4
7	7	7 - 6 = 1	(1)² = 1
8	5	5 - 6 = -1	(-1)² = 1
9	4	4 - 6 = -2	(-2)² = 4
10	5	5 - 6 = -1	(-1)² = 1
n = 10	Sum = 60		Σ (X - μ)² = 26

Step #3: Calculate the variance.

This step depends on whether or not the set you are working with represents the total data (population) or partial data (sample). Here is how you calculate the variance from the results in step #2 for either case (μ and X are both symbols for Mean, with the only real difference indicated by red text):

Population Variance (σ²)
σ² =	Σ (X - μ)²	=	26	= 2.60
	n		10

Sample Variance (s²)
s² =	Σ (X - X)²	=	26	= 2.89
	n - 1		9

Step #4: Calculate the square root of the variance.

This step is basically the same for both the population and the sample standard deviation calculations. The only difference is that the Variance was computed differently in Step #3 (n in denominator vs n - 1):