Page 398 - Math Smart - 7

Estimated mean for grouped data

Grouped data is represented in a frequency table. The estimated mean is
calculated by dividing the sum of f.\ by the sum of/in a frequency table.
estimated mean = sum of/v
sum of/

Calculate an estimate for the mean of the grouped data.

Mass Frequency
(kg) (/)

30 < m s40 15
40 < m £ 50 28
50 < m £ 60 12
60 < m £ 70 10
80 < m £ 90 8
90 < m £ 100 5

Solutioii
Mass (kg) Midpoint (m) Frequency (/) /m
The midpoint of the class
interval in the first row is 30 < m £ 40 ^ 15 525
35
calculated by: '4(r<rrr£ 50 45 28 1260
30 + 40 50 < m £ 60 55 12 660
= 35
2
60 < m £ 70 65 10 650
70 < m £ 80 75 8 600
80 < m £ 90 85 5 425
Total 78 4120

estimated mean = sum of/a-
sum of/
- 4120
78
= 52.82

The estimated mean for the grouped data is 52.82 kg.

The frequency table shows the number of strawberry
Number of
shrubs in a nursery with different numbers of 0-9 10-19 20-29 30-39
strawberries
strawberries growing on each shrub.
Frequency 6 8 4 2
a) How many shrubs are there in this nursery?
b) What is the modal class of the grouped data?
c) Calculate an estimate of the mean number of strawberries.

394 UNIT 17