Question

the monthly salaries (in thousands of dollars) of a sample of 6 sales representatives are as follows. 9, 11, 12, 13, 8, 13 send data to calculator find the standard deviation of this sample of monthly salaries. round your answer to two decimal places. (if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate the mean

The data set is \( 9, 11, 12, 13, 8, 13 \). The number of data points \( n = 6 \).
The mean \( \bar{x}=\frac{9 + 11+12 + 13+8 + 13}{6}=\frac{66}{6} = 11 \).

Step2: Calculate the squared differences

For each data point \( x_i \), calculate \( (x_i-\bar{x})^2 \):

• For \( x = 9 \): \( (9 - 11)^2=(- 2)^2 = 4 \)
• For \( x = 11 \): \( (11 - 11)^2=0^2 = 0 \)
• For \( x = 12 \): \( (12 - 11)^2=1^2 = 1 \)
• For \( x = 13 \): \( (13 - 11)^2=2^2 = 4 \)
• For \( x = 8 \): \( (8 - 11)^2=(-3)^2 = 9 \)
• For \( x = 13 \): \( (13 - 11)^2=2^2 = 4 \)

Step3: Calculate the sum of squared differences

Sum of \( (x_i-\bar{x})^2 \) is \( 4+0 + 1+4+9+4=22 \).

Step4: Calculate the sample variance

Sample variance \( s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{22}{6 - 1}=\frac{22}{5}=4.4 \).

Step5: Calculate the sample standard deviation

Sample standard deviation \( s=\sqrt{s^2}=\sqrt{4.4}\approx2.0976\approx2.10 \) (rounded to two decimal places).

Answer:

\( 2.10 \)