6.2 Mode and Mean of Grouped Data (Examples)

Example:
The following frequency table shows the number of magazines sold at a bookshop for 30 days in April 2013.

Number of magazines
Frequency
220 – 229
3
230 – 239
5
240 – 249
11
250 – 259
6
260 – 269
5
Based on the data given,
(a) calculate the size of class,
(b) state the modal class,
(c) calculate the mean number of magazine sold per day. 
 
Solution:
(a) Size of the class
  = upper boundary – lower boundary
  = 229.5 – 219.5
  = 10
 
(b) Modal class = 240 – 249 (Highest frequency)
 
(c)
Number of magazines
Frequency (f)
Class midpoint (x)
220 – 229
3
224.5
230 – 239
5
234.5
240 – 249
11
244.5
250 – 259
6
254.5
260 – 269
5
264.5
 
Midpoint= 220+229 2 =224.5 mean,  x ¯ = fx f 3×224.5+5×234.5+11×244.5+6×254.5+5×264.5 30 = 7385 30 =246.2