How to find the mean and standard deviation for age...

Question

e following data represent the number of people aged 25 to 64 years covered by health insurance (private or government) in 2003. Approximate the mean and standard deviation for age.

 

Age    Number (millions)

25-34   22.2

35-44   33.4

45-54   35.6

55-64   26.4

Answer 1

First you find the median (middle) of each age category:

29.5, 39.5, 49.5, 59.5

That is 4.5 years more than the lower bound, and 4.5 less than the

upper bound of each category.

The sample size in millions is 22.2+33.4+35.6 + 26.4 = 117.6 million

Next, multiplies the median ages by the corresponding frequencies:

29.5 * 22.2 + 39.5 * 33.4 + 49.5 * 35.6 + 59.5 * 26.4 = 5307.2 million

The average is then 5307.2 / 117.6 = 45.129251700680272....