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 ​25-34 ​35-44 ​45-54 ​55-64 Number​ (millions) 22.3 34.4 35.4 28.9

Answer 1

Solution:

If we make a frequency distribution of age it will be as follows:

Age	frequency (f)
25 - 34	22.3
35 - 44	34.4
45 - 54	35.4
55 - 64	28.9

The mean of the grouped frequency distribution is given as follows:

Where, f_{​​​​​​i}​​​'s are frequencies and x_{​​​​​​i}​​​'s are mid point of the intervals.

Mid-point = (lower limit + upper limit)/2

Age	frequency (f​​​​​​i)	x​​​​​​i	f​​​​i x​​​​​​i
25 - 34	22.3	(25+34)/2 = 29.5	657.85
35 - 44	34.4	(35+44)/2 = 39.5	1358.8
45 - 54	35.4	(45+54)/2 = 49.5	1752.3
55 - 64	28.9	(55+64)/2 = 59.5	1719.55
Total	121		5488.5

From the above table we have,

The mean age is 45.36 years.

For grouped frequency distribution, the standard deviation is given as follows:

Where,

frequency (f​​​​​​i)	x​​​​​​i	f​​​​i x​​​​​​i	f​​​​​​i xi​​​​​​2
22.3	(25+34)/2 = 29.5	657.85	19406.575
34.4	(35+44)/2 = 39.5	1358.8	53672.6
35.4	(45+54)/2 = 49.5	1752.3	86738.85
28.9	(55+64)/2 = 59.5	1719.55	102313.23
Total = 121	Total	5488.5	262131.5

From the above table we have,

The standard deviation of age is 10.535 years.

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