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Sagot :
The sample deviation of a distribution is the square root of the variance
- The average age of the distribution is 37.26
- The sample standard deviation is 21.27
How to calculate the average age
Using a midpoint of 10 for the first class, and 75 for the last, we have the following frequency distribution:
Age Percentage
10 20
15.5 5
21 10
29.5 13
39.5 15
54.5 25
75 12
The average age is then calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) =10 * 20\% + 15.5* 5\% + 21 * 10\% + 29.5*13\% + 39.5*15\% + 54.5 * 25\% + 75 *12\%[/tex]
[tex]E(x) =37.26[/tex]
Hence, the average age of the distribution is 37.26
How to calculate the sample standard deviation
This is calculated using:
[tex]\sigma = \sqrt{E(x^2) - E(x)^2}[/tex]
Where:
[tex]E(x^2) =10^2 * 20\% + 15.5^2* 5\% + 21^2 * 10\% + 29.5^2*13\% + 39.5^2*15\% + 54.5^2 * 25\% + 75^2 *12\%[/tex]
Evaluate the products
[tex]E(x^2) =1840.845[/tex]
The equation becomes
[tex]\sigma = \sqrt{1840.845- 37.26^2}[/tex]
[tex]\sigma = 21.27[/tex]
Hence, the sample standard deviation is 21.27
Read more about average and sample standard deviation at:
https://brainly.com/question/15858152
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