The following data set represents the number of employees in each of the eight divisions at a medium-sized local Find the variance for this data set of numbers: 15, 24, 22, 25, 78, 36, 22, 42 • Round the final answer to one decimal place.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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### Calculating Variance for a Data Set

#### Example Problem:
The following data set represents the number of employees in each of the eight divisions at a medium-sized local business:

**Data Set:**
15, 24, 22, 25, 78, 36, 22, 42

**Task:**
Find the variance for this data set of numbers.

**Instructions:**
- Round the final answer to one decimal place.

#### Solution Steps:
1. **Calculate the Mean (Average)**:
   - Add all the numbers together.
   - Divide by the total number of values in the data set.

2. **Calculate Each Data Point's Deviation from the Mean**:
   - Subtract the mean from each number to find the deviation for each data point.

3. **Square Each Deviation**:
   - Square each deviation to eliminate negative values.

4. **Find the Average of These Squared Deviations**:
   - Add the squared deviations together.
   - Divide by the total number of values to obtain the variance.

**Note:** In this example, the data set is small enough to demonstrate the calculation manually, but for larger sets, you may want to use statistical software or a calculator.

By following these steps, you will be able to determine the variance of the employees' data set. Remember to round your final answer to one decimal place to meet the problem's requirements.
Transcribed Image Text:### Calculating Variance for a Data Set #### Example Problem: The following data set represents the number of employees in each of the eight divisions at a medium-sized local business: **Data Set:** 15, 24, 22, 25, 78, 36, 22, 42 **Task:** Find the variance for this data set of numbers. **Instructions:** - Round the final answer to one decimal place. #### Solution Steps: 1. **Calculate the Mean (Average)**: - Add all the numbers together. - Divide by the total number of values in the data set. 2. **Calculate Each Data Point's Deviation from the Mean**: - Subtract the mean from each number to find the deviation for each data point. 3. **Square Each Deviation**: - Square each deviation to eliminate negative values. 4. **Find the Average of These Squared Deviations**: - Add the squared deviations together. - Divide by the total number of values to obtain the variance. **Note:** In this example, the data set is small enough to demonstrate the calculation manually, but for larger sets, you may want to use statistical software or a calculator. By following these steps, you will be able to determine the variance of the employees' data set. Remember to round your final answer to one decimal place to meet the problem's requirements.
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