Question

The following data represent the number of people aged 25 to 64 years covered by health insurance​ (private or​ government) in 2018. Approximate the mean and standard deviation for age.
Age Lower Limit Upper Limit Number (millions)
25-34 25 34 26200000
35-44 35 44 33800000
45-54 45 54 33100000
55-64 55 64 29600000

Answer 1

Answer:

X=∑fX ∑f , where ¯X is the mean.

Mean = 115/4 = 28.75

Standard deviation = $\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}$     n = the number of items = 4

Standard deviation = √28.37/4 = √7.0925 = 2.66317

Step-by-step explanation:

Mean is the number which is obtained by adding the values of all the items of a series and dividing the total by the number of items.

Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values

So, Class intervals are given here.

We have to find the middle point of the class interval.

So,

Class interval= 25- 34

Middle point= $\frac{34-25}{2}$= $\frac{9}{2}= 4.5$

Let's add 4.5 to the lower interval,

=> 25 + 4.5= 29.5

This is the median point and do the same for the other intervals too

i.e 39.5,49.5 and then 59.5 then multiply the number with the middle point.

So midpoint times the number. So, we get

29.5 * 21.7 = 640.15 & so on we get 129,...

Then add these numbers together. So that becomes 5375.75. And what about the total number here, that is

=>21.7 + 32.8 + 36.8 + 21.7= 118.5

So here,

Mean value, that should be equal to the sum of mean times the number divided by the total number here,

Mean= $\frac{5375.75}{118.5}$ = 45.36

So, this is the mean value.

Standard deviation:

Standard deviation =  $\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}$

$\sigma$ = population standard deviation

N = the size of the population

$x_{i}$ = each value from the population

$\mu$ = the population mean

So here is what we have to do,

We have to subtract the mean value from the middle point that is,

=>45.36- 21.5 and squared plus 45.36 -39.5 Squared. And plus this is 45.36 -49.5 Squared plus 45.36 -59.5 squared. And then, this is 45.

Let me just inside the apprentices Inside the practices, this is 45 .36 29.5 and take the square of this one And then add another one Which is 45.36 39.5 and then take the square this one too. And plus inside parentheses, this is 45.36 minus Which is 490.5 And then squared. That is 45.36 And -59 0.5 so And then take the square, there's 12 if you just add all of them, so we will get five 47.1184.

So the standard deviation is the square of 547, divided by The total frequency here.

Standard deviation = √28.37/4 = √7.0925 = 2.66317

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