Question

part 1 of 2
completed: 2 of 7 my score: 2/7 pts
find the sample variance and standard deviation.
7, 46, 14, 51, 38, 22, 31, 27, 35, 26
choose the correct answer below. fill in the answer box to complete your choice.
(round to two decimal places as needed.)
a. $s^{2} = \square$
b. $\sigma^{2} = \square$

Explanation:

Step1: Calculate sample mean

First, sum all values and divide by sample size $n=10$.
$\bar{x} = \frac{7+46+14+51+38+22+31+27+35+26}{10} = \frac{297}{10} = 29.7$

Step2: Compute squared deviations

Find $(x_i - \bar{x})^2$ for each value:
$(7-29.7)^2=515.29$, $(46-29.7)^2=265.69$, $(14-29.7)^2=246.49$, $(51-29.7)^2=453.69$, $(38-29.7)^2=68.89$, $(22-29.7)^2=59.29$, $(31-29.7)^2=1.69$, $(27-29.7)^2=7.29$, $(35-29.7)^2=28.09$, $(26-29.7)^2=13.69$

Step3: Sum squared deviations

Add all squared deviations together.
$\sum(x_i - \bar{x})^2 = 515.29+265.69+246.49+453.69+68.89+59.29+1.69+7.29+28.09+13.69 = 1660.1$

Step4: Calculate sample variance

Use sample variance formula $s^2=\frac{\sum(x_i - \bar{x})^2}{n-1}$.
$s^2 = \frac{1660.1}{10-1} = \frac{1660.1}{9} \approx 184.46$

Answer:

A. $s^2 = 184.46$