# Measure of variation standard deviation s q x x 2 n 1

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Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:x=1 + 3 + 143=183= 6.0Step 2:
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:x=1 + 3 + 143=183= 6.0Step 2:xx-x(x-x)2
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:x=1 + 3 + 143=183= 6.0Step 2:xx-x(x-x)211-6 =-5(-5)2= 25
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:x=1 + 3 + 143=183= 6.0Step 2:xx-x(x-x)211-6 =-5(-5)2= 2533-6 =-3(-3)2= 9
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:x=1 + 3 + 143=183= 6.0Step 2:xx-x(x-x)211-6 =-5(-5)2= 2533-6 =-3(-3)2= 91414-6 = 8(8)2= 64
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:x=1 + 3 + 143=183= 6.0Step 2:xx-x(x-x)211-6 =-5(-5)2= 2533-6 =-3(-3)2= 91414-6 = 8(8)2= 64(x-x)2=25 + 9 + 64 = 98Step 3:
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:x=1 + 3 + 143=183= 6.0Step 2:xx-x(x-x)211-6 =-5(-5)2= 2533-6 =-3(-3)2= 91414-6 = 8(8)2= 64(x-x)2=25 + 9 + 64 = 98Step 3:s=r(x-x)2n-1
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14
Measure of Variation: Standard deviations=q(x-x)2n-1Example:Find the standard deviationsof the data 1, 3, 14Step 1: find the mean:x=1 + 3 + 143=183= 6.0Step 2:xx-x(x-x)211-6 =-5(-5)2= 2533-6 =-3(-3)2= 91414-6 = 8(8)2= 64(x-x)2=25 + 9 + 64 = 98Step 3:s=r(x-x)2n-1=s98(3-1)=49 = 7
Measure of Variation: Standard deviationThere is another formula to find the standard deviations, which isconsidered the short-cut formula:s=sn(x)2-(x)2n(n-1)whereX(x)2:square each data, and then add them up.Xx2:add up all the data, and then square it
Measure of Variation: Standard deviations=qn(x)2-(x)2n(n-1)Example:Use the short-cut formula to findsof the data 1, 3, 14
Measure of Variation: Standard deviations=qn(x)2-(x)2n(n-1)Example:Use the short-cut formula to findsof the data 1, 3, 14Step 1:x(x)2112= 1332= 914142= 196x= 18(x)2= 206
Measure of Variation: Standard deviations=qn(x)2-(x)2n(n-1)Example:Use the short-cut formula to findsof the data 1, 3, 14Step 1:x(x)2112= 1332= 914142= 196x= 18(x)2= 206Step 2:s=sn(x)2-(x)2n(n-1)