Question

compute the standard deviation for the set of data.
2, 5, 6, 8, 14
a. 16
c. 80
b. 4
d. 2
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{2 + 5+6 + 8+14}{5}=\frac{35}{5}=7$

Step2: Calculate the squared differences

$(2 - 7)^2=( - 5)^2 = 25$; $(5 - 7)^2=( - 2)^2 = 4$; $(6 - 7)^2=( - 1)^2 = 1$; $(8 - 7)^2=1^2 = 1$; $(14 - 7)^2=7^2 = 49$

Step3: Calculate the variance

The variance $s^{2}=\frac{25 + 4+1 + 1+49}{5}=\frac{80}{5}=16$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{16}=4$

Answer:

B