Question

the following four sets of 7 numbers all have a mean of 9. complete parts (a) through (d) below. {9,9,9,9,9,9,9} , {8,8,9,9,9,10,10} , {6,6,6,9,12,12,12} , {4,4,4,9,14,14,14}... a. b. c. d. c. compute the standard deviation for each set. compute the standard deviation for set {9,9,9,9,9,9,9}. s = (round to the nearest tenth as needed.)

Explanation:

Step1: Recall the formula for sample standard deviation

The formula for the sample standard deviation \( s \) is \( s = \sqrt{\frac{\sum_{i = 1}^{n}(x_i - \bar{x})^2}{n - 1}} \), where \( n \) is the number of data points, \( x_i \) are the individual data points, and \( \bar{x} \) is the mean.

Step2: Identify values for the set \(\{9,9,9,9,9,9,9\}\)

Here, \( n = 7 \), \( \bar{x}=9 \), and each \( x_i = 9 \). So for each \( i \), \( x_i-\bar{x}=9 - 9=0 \).

Step3: Calculate the sum of squared deviations

\(\sum_{i = 1}^{7}(x_i - \bar{x})^2=\sum_{i = 1}^{7}(0)^2=0\).

Step4: Substitute into the standard deviation formula

\( s=\sqrt{\frac{0}{7 - 1}}=\sqrt{0}=0 \).

Answer:

\( 0.0 \)