MATLAB: An Introduction with Applications
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![### Determining Statistical Values from a Population Data Set
The numbers of regular season wins for 10 football teams in a given season are provided below. The goal is to determine the range, mean, variance, and standard deviation of this population data set.
Given data set:
\[2, 7, 15, 4, 14, 6, 13, 8, 3, 10\]
**Step-by-Step Solution:**
1. **Range:**
- The range is the difference between the maximum and minimum values in the dataset.
- From the given data:
\[
\text{Maximum value} = 15, \quad \text{Minimum value} = 2
\]
- Therefore, the range is:
\[
\text{Range} = 15 - 2 = 13
\]
- The range is \(13\)
2. **Mean (Average):**
- The mean is the sum of all values divided by the number of values.
- Sum of the data set:
\[
2 + 7 + 15 + 4 + 14 + 6 + 13 + 8 + 3 + 10 = 82
\]
- Number of values:
\[
n = 10
\]
- Therefore, the mean is:
\[
\text{Mean} = \frac{82}{10} = 8.2
\]
- The population mean is \(8.2\)
3. **Variance:**
- Variance is the average of the squared differences from the mean.
- Steps to calculate variance:
1. Calculate the mean (already found to be 8.2).
2. Subtract the mean from each data value and square the result:
\[
(2 - 8.2)^2, (7 - 8.2)^2, (15 - 8.2)^2, (4 - 8.2)^2, (14 - 8.2)^2, (6 - 8.2)^2, (13 - 8.2)^2, (8 - 8.2)^2, (3 - 8.2)^2, (10 - 8.2)^2
\]](https://content.bartleby.com/qna-images/question/5c7c62dd-c6b1-40a7-b3f4-b34aa766f300/04daba98-1dd1-4c09-9ded-c935940e8d11/oxw701_reoriented.jpeg)
Transcribed Image Text:### Determining Statistical Values from a Population Data Set
The numbers of regular season wins for 10 football teams in a given season are provided below. The goal is to determine the range, mean, variance, and standard deviation of this population data set.
Given data set:
\[2, 7, 15, 4, 14, 6, 13, 8, 3, 10\]
**Step-by-Step Solution:**
1. **Range:**
- The range is the difference between the maximum and minimum values in the dataset.
- From the given data:
\[
\text{Maximum value} = 15, \quad \text{Minimum value} = 2
\]
- Therefore, the range is:
\[
\text{Range} = 15 - 2 = 13
\]
- The range is \(13\)
2. **Mean (Average):**
- The mean is the sum of all values divided by the number of values.
- Sum of the data set:
\[
2 + 7 + 15 + 4 + 14 + 6 + 13 + 8 + 3 + 10 = 82
\]
- Number of values:
\[
n = 10
\]
- Therefore, the mean is:
\[
\text{Mean} = \frac{82}{10} = 8.2
\]
- The population mean is \(8.2\)
3. **Variance:**
- Variance is the average of the squared differences from the mean.
- Steps to calculate variance:
1. Calculate the mean (already found to be 8.2).
2. Subtract the mean from each data value and square the result:
\[
(2 - 8.2)^2, (7 - 8.2)^2, (15 - 8.2)^2, (4 - 8.2)^2, (14 - 8.2)^2, (6 - 8.2)^2, (13 - 8.2)^2, (8 - 8.2)^2, (3 - 8.2)^2, (10 - 8.2)^2
\]
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