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The estimated distribution (in millions) of the population by age in a certain country for the year 2015 is shown in the
pie chart. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the
sample standard deviation of the data set. Use 70 as the midpoint for "65 years and over."
The sample mean is x- (Round to two decimal places as needed.)
Under 4 years: 24.8
15-14 years: 422
15-19 years 194
20-24 years: 256
25-34 years 50.7
35-44 years: 35.7
45-64 years 75.2
65 years and over 54.3

Sagot :

MrRoyal

The sample mean for the data is 21.38 and the sample standard deviation for the data is 56.19

The frequency distribution for the data

To do this, we start by calculating the midpoint of each class using:

Midpoint= (Lower + Upper)/2

Using the above formula, we have:

Age (x)        Frequency (f)

2                   24.8

9.5               422

17                  194

22                 256

29.5             50.7

39.5              35.7

54.5             75.2

70                 54.3

The sample mean for the data

This is calculated using:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{2*24.8 + 9.5*422 + 17*194 + 22*256 + 29.5*50.7 + 39.5*35.7 + 54.5*75.2+70*54.3}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3}[/tex]

Evaluate

[tex]\bar x = \frac{23793.8}{1112.7}[/tex]

[tex]\bar x = 21.38[/tex]

Hence, the sample mean for the data is 21.38

The sample standard deviation for the data

This is calculated using:

[tex]\sigma_x = \sqrt{\frac{\sum f(x- \bar x)^2}{\sum f - 1}}[/tex]

So, we have:

[tex]\sigma_x = \sqrt{\frac{2*(24.8-21.38)^2 + .............+70*(54.3-21.38)^2}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3 - 1}}[/tex]

Evaluate

[tex]\sigma_x = \sqrt{\frac{3509508.4556}{1111.7}}[/tex]

[tex]\sigma_x = \sqrt{3156.88446128}[/tex]

[tex]\sigma_x = 56.19[/tex]

Hence, the sample standard deviation for the data is 56.19

Read more about mean and standard deviation at:

https://brainly.com/question/15858152

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