Question

compute the standard deviation for the set of data. 13.3, 14.3, 15.3, 16.3, 17.3 a. $sqrt{2}$ b. 2 c. $sqrt{10}$ d. 4 please select the best answer from the choices provided

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{13.3 + 14.3+15.3+16.3+17.3}{5}=\frac{76.5}{5}=15.3$

Step2: Calculate the squared - differences

$(13.3 - 15.3)^2=(- 2)^2 = 4$
$(14.3 - 15.3)^2=(-1)^2 = 1$
$(15.3 - 15.3)^2=0^2 = 0$
$(16.3 - 15.3)^2=1^2 = 1$
$(17.3 - 15.3)^2=2^2 = 4$

Step3: Calculate the variance

The variance $s^{2}=\frac{4 + 1+0+1+4}{5}=\frac{10}{5}=2$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{s^{2}}=\sqrt{2}$

Answer:

A. $\sqrt{2}$