Answer :

Sure! To estimate the variance of the given data set [tex]\(5, 8, 10, 15, 22\)[/tex], follow these steps:

1. Calculate the Mean:
To find the mean, add up all the numbers in the data set and divide by the total number of values.

[tex]\[
\text{Mean} = \frac{5 + 8 + 10 + 15 + 22}{5} = \frac{60}{5} = 12.0
\][/tex]

2. Calculate Each Deviation from the Mean:
Subtract the mean from each number in the data set to find each deviation.

- [tex]\(5 - 12 = -7\)[/tex]
- [tex]\(8 - 12 = -4\)[/tex]
- [tex]\(10 - 12 = -2\)[/tex]
- [tex]\(15 - 12 = 3\)[/tex]
- [tex]\(22 - 12 = 10\)[/tex]

3. Square Each Deviation:
Square each deviation to eliminate negative values and emphasize larger deviations.

- [tex]\((-7)^2 = 49\)[/tex]
- [tex]\((-4)^2 = 16\)[/tex]
- [tex]\((-2)^2 = 4\)[/tex]
- [tex]\(3^2 = 9\)[/tex]
- [tex]\(10^2 = 100\)[/tex]

4. Calculate the Mean of the Squared Deviations:
Add all the squared deviations together and then divide by the number of data values to find the variance.

[tex]\[
\text{Variance} = \frac{49 + 16 + 4 + 9 + 100}{5} = \frac{178}{5} = 35.6
\][/tex]

So, the variance of the data set is 35.6.

Thanks for taking the time to read Example 4 3 Estimate the variance of the following data set tex 5 8 10 15 22 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada