Theory question 106
StatisticsThe table shows the distribution of the ages of a group of people in a village.
Ages (in years): 15 − 18, 19 − 22, 23 − 26, 27 − 30, 31 − 34, 35 − 38
Freq.: 40, 33, 25, 10, 8, 4
Using an assumed mean of 24.5, calculate the mean of the distribution.
Show the model answer
Model answer
Class midpoints: 16.5, 20.5, 24.5, 28.5, 32.5, 36.5
d = x − 24.5: −8, −4, 0, 4, 8, 12
fd: −320, −132, 0, 40, 64, 48
Σf = 120, Σfd = −300
Mean = 24.5 + (−300/120) = 24.5 − 2.5 = 22 years
Explanation
Mean = assumed mean + Σfd/Σf.