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QuestionFind the standard deviation of the monthly salaries (in \1000s):1000s): 8, 13, 11, 12, 6, 10$. Round to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The monthly salaries of the sales representatives are given as 8k,8k, 13k, 11k,11k, 12k, 6k,6k, 10k. . We need to find the standard deviation of these salaries.
3. The standard deviation is a measure of how spread out numbers are. It is the square root of the Variance.
4. Variance is the average of the squared differences from the Mean.

STEP 2

First, we need to find the mean (average) of the salaries. We can do this by adding up all the salaries and then dividing by the number of salaries.
Mean=Sum of salariesNumber of salariesMean = \frac{Sum\, of\, salaries}{Number\, of\, salaries}

STEP 3

Now, plug in the given values for the salaries and their count to calculate the mean.
Mean=8+13+11+12+6+106Mean = \frac{8+13+11+12+6+10}{6}

STEP 4

Calculate the mean salary.
Mean=606=10Mean = \frac{60}{6} =10

STEP 5

Next, we need to find the variance. This is done by subtracting the mean from each salary, squaring the result, and then averaging these squared results.
Variance=Sum of (Salary−Mean)2Number of salariesVariance = \frac{Sum\, of\, (Salary - Mean)^2}{Number\, of\, salaries}

STEP 6

Now, plug in the given values for the salaries, their count, and the mean to calculate the variance.
Variance=(8−10)2+(13−10)2+(11−10)2+(12−10)2+(6−10)2+(10−10)26Variance = \frac{(8-10)^2+(13-10)^2+(11-10)^2+(12-10)^2+(6-10)^2+(10-10)^2}{6}

STEP 7

Calculate the variance.
Variance=4+9+1+4+16+06=346=5.67Variance = \frac{4+9+1+4+16+0}{6} = \frac{34}{6} =5.67

STEP 8

Finally, we find the standard deviation by taking the square root of the variance.
Standard Deviation=VarianceStandard\, Deviation = \sqrt{Variance}

STEP 9

Plug in the value for the variance to calculate the standard deviation.
Standard Deviation=5.67Standard\, Deviation = \sqrt{5.67}

STEP 10

Calculate the standard deviation and round to two decimal places.
Standard Deviation=2.38Standard\, Deviation =2.38The standard deviation of the monthly salaries is $2.38k.

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