Question

find the standard deviation of the sample data set. 51 64 35 74 42 62 34 39 52 77 (1 point) 3.8 15.7 247.3 14.9

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{51 + 64+35+74+42+62+34+39+52+77}{10}=\frac{530}{10} = 53$

Step2: Calculate the squared differences

$(51 - 53)^2=(-2)^2 = 4$; $(64 - 53)^2 = 11^2=121$; $(35 - 53)^2=(-18)^2 = 324$; $(74 - 53)^2=21^2 = 441$; $(42 - 53)^2=(-11)^2 = 121$; $(62 - 53)^2=9^2 = 81$; $(34 - 53)^2=(-19)^2 = 361$; $(39 - 53)^2=(-14)^2 = 196$; $(52 - 53)^2=(-1)^2 = 1$; $(77 - 53)^2=24^2 = 576$

Step3: Calculate the variance

The sample variance $s^{2}=\frac{4 + 121+324+441+121+81+361+196+1+576}{10 - 1}=\frac{2226}{9}\approx247.33$

Step4: Calculate the standard deviation

The sample standard deviation $s=\sqrt{247.33}\approx15.7$

Answer:

15.7