what is the standard deviation for the data given: {12, 13, 29, 18, 61, 35, 21}

Explanation:

Step1: Calculate the mean

The data set is (x = {12,13,29,18,61,35,21}). The number of data - points (n = 7). 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