Question

As the head of public health, you conduct a weekly census across age-groups of the number of cases of flu reported in your area. By hand, compute the mean and the median by week. Which do you think, given these particular data, is the most useful measure of central tendency and why?

12/1-through 12/7 12/ 8 through 12/15 12/16 through 12/23

0-4 years 12 14 15

5- 9 years 15 12 14

10-14 years 12 24 21

15- 19 years 38 12 19

Mean

Median .

Answer 1

Calculating Mean for the entire period:

Frequency for 0-4 is 41

Frequency for 5-9 is 41

Frequency for 10-14 is 57

Frequency for 15-19 is 69

Now we calculate mid points

0-4 = 2
5-9 = 7
10-14 = 12
15-19 = 17

Now we multiply mid points with the frequencies for respective class intervals. Dividing it by sum of frequencies gives us the mean.
I.e (2*41 + 7*41 + 12*57 + 17*69)/38

Mean = 58.57 per month or 14.64 per week

Calculation of median

By median, we mean the middle value, which is the 19th value which belongs to class interval 10-14. We make the class intervals continuous to solve this question by subtracting 0.5 from the lower class interval and adding 0.5 to upper class interval.
Estimated median = Lower Class interval for the median group + (Frequency/2 - Sum of frequencies of previous class intervals)/Frequency of median group*Width

Our estimated median is 9.5 + (38/2 - 9)/12*5

= 13.667

Median is a more useful measure of central tendency as median unlike a mode is not very much affected by the ouliers of the sample data. It gives true central value for any distribution.