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Calculate the population standard deviation of the data 13, 17, 23, 26, 31, 28, 15, 34, 17, and 26. (Round off your answer to two decimal places.) 7286
7.18
7.26
6.81
6.19
6.81
Calculate the mean first, then use the variance shortcut formula σ2=n∑xi2−x2. This avoids repeated subtraction errors.
A data set of 10 values: 13, 17, 23, 26, 31, 28, 15, 34, 17, and 26.
σ=n∑i=1n(xi−x)2
Calculate the mean first, then use the variance shortcut formula σ2=n∑xi2−x2. This avoids repeated subtraction errors.
Confusing 'Population Standard Deviation' (divide by n=10) with 'Sample Standard Deviation' (divide by n−1=9), which leads to an incorrect higher value.
Calculate the mean
Sum of all values is 13+17+23+26+31+28+15+34+17+26=230. The mean is 230/10=23.
x=23
Calculate squared deviations from mean
Subtract mean from each value and square: (13−23)2=100,(17−23)2=36,(23−23)2=0,(26−23)2=9,(31−23)2=64,(28−23)2=25,(15−23)2=64,(34−23)2=121,(17−23)2=36,(26−23)2=9.
∑(xi−x)2=464
Calculate variance and standard deviation
Divide sum of squares by n=10 to get variance σ2=46.4, then take the square root.
σ=46.4≈6.8117
C is correct because the square root of the variance (46.4) equals approximately 6.81.
Standard deviation is the square root of variance, a concept frequently tested in Data Interpretation sections of competitive exams to measure data dispersion.
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