The following frequency table summarizes the ages of 60 shoppers at the local grocery store. Calculate the approximate sample mean for this data (mean for the grouped data).
A)37.50 years
B)36.25 years
C)32.25 years
D)40.25 years
E)45.50 years

Question

The following frequency table summarizes the ages of 60 shoppers at the local grocery store.  Calculate the approximate sample mean for this data (mean for the grouped data).
A)37.50 years 
B)36.25 years 
C)32.25 years 
D)40.25 years 
E)45.50 years

Quizplus · Accepted Answer

To find the approximate sample mean for grouped data, we use the midpoint of each interval as the representative value for that interval. We can create a new table with an additional column for the midpoints:

Age Range | Frequency | Midpoint 
----------|-----------|--------- 
20-24     | 7         | 22 
25-29     | 13        | 27 
30-34     | 16        | 32 
35-39     | 14        | 37 
40-44     | 6         | 42 
45-49     | 4         | 47

The approximate sample mean is then calculated as the sum of (frequency * midpoint) divided by the total frequency:

((7*22) + (13*27) + (16*32) + (14*37) + (6*42) + (4*47)) / 60 = 36.25

Therefore, the best choice is B.

The Following Frequency Table Summarizes the Ages of 60 Shoppers