Question

what is the standard deviation for the data given: {12, 13, 29, 18, 61, 35, 21} 6/13 293.67 17.14 15.87 41.98

Explanation:

Step1: Calculate the mean

The data set is \(x = \{12,13,29,18,61,35,21\}\). The mean \(\bar{x}=\frac{12 + 13+29+18+61+35+21}{7}=\frac{189}{7}=27\).

Step2: Calculate the squared - differences

\((12 - 27)^2=(- 15)^2 = 225\), \((13 - 27)^2=(-14)^2 = 196\), \((29 - 27)^2=2^2 = 4\), \((18 - 27)^2=(-9)^2 = 81\), \((61 - 27)^2=34^2 = 1156\), \((35 - 27)^2=8^2 = 64\), \((21 - 27)^2=(-6)^2 = 36\).

Step3: Calculate the variance

The variance \(s^{2}=\frac{225 + 196+4+81+1156+64+36}{7}=\frac{1762}{7}\approx251.71\).

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{\frac{1762}{7}}\approx15.87\).

Answer:

15.87