Question

construct a data set that has the given statistics.

n = 7
\\( \overline { x } = 13 \\)
\\( s = 0 \\)

a. the number of values in the sample data set.
b. the difference between all the values in the sample data.
c. the range of the sample data set.
d. the mean of the sample data set.

this means there should be 7 values in the sample data set.

what does the value \\( \overline { x } \\) mean?

a. the mean of the sample data set.
b. the range of the sample data set.
c. the difference between all the values in the sample data.
d. the most common value in the sample data.

this means the sample mean of the 7 values in the sample data should be 13.

what does the value s mean?

a. the spread of the data from the sample mean.
b. the range of the sample data set.
c. the most common value in the sample data.
d. the number of values that equal the sample mean.

Explanation:

Step1: Recall the formula for standard deviation

The formula for the sample standard deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}\). If \(s = 0\), then \(\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}=0\).

Step2: Analyze the condition for \(\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}=0\)

Since \((x_{i}-\bar{x})^{2}\geq0\) for all \(i\), the only way \(\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}=0\) is when \(x_{i}-\bar{x}=0\) for all \(i = 1,2,\cdots,n\). That is \(x_{i}=\bar{x}\) for all \(i\).

Step3: Construct the data - set

Given \(n = 7\) and \(\bar{x}=13\), the data - set is \(\{13,13,13,13,13,13,13\}\)

Answer:

The data set is \(\{13,13,13,13,13,13,13\}\)