5.3. Grouped Data to Find the Mean http://www.ck12.org
Example C
The ages of 100 singers of a 360-member choir are shown in the table below:
TABLE5.11:
Ages of Members (years) Number of Members
20 to less than 25 12
25 to less than 30 14
30 to less than 35 10
35 to less than 40 8
40 to less than 45 20
45 to less than 50 6
50 to less than 55 5
55 to less than 60 4
60 to less than 65 11
65 to less than 70 10Calculate the mean of the ages.
First create the table below:
TABLE5.12:
Ages of Members (years) Number of Membersf Midpoint Of Classm Productm f
20 to less than 25 12 22.5 270.0
25 to less than 30 14 27.5 385.0
30 to less than 35 10 32.5 325.0
35 to less than 40 8 37.5 300.0
40 to less than 45 20 42.5 850.0
45 to less than 50 6 47.5 285.0
50 to less than 55 5 52.5 262.5
55 to less than 60 4 57.5 230.0
60 to less than 65 11 62.5 687.5
65 to less than 70 10 67.5 675.0Since the ages represent a sample, the mean can be calculated as shown:
x=
∑m f
n
x=270. 0 + 385. 0 + 325. 0 + 300. 0 + 850. 0 + 285. 0 + 262. 5 + 230. 0 + 687. 5 + 675. 0
100
x=4 , 270. 0
100
x= 42. 7The mean age of the 100 members of the choir is 42.7 years.
Points to Consider
- Is the mean only used as a measure of central tendency, or is it applied to other representations of data?
- If the mean is applied to other representations of data, can its value be calculated or estimated from this
representation?