Grouped Frequency

Calculating an estimate of the mean

Jill Robertson

Which is the modal class?

Weight 61 – 65 66 – 70 71 – 75 76 –80 81 - 85

Freq. 9 20 29 15 7

71 - 75

Question 1

A gardener checks the weights (in grams) of a number of tomatoes for grading purposes. Here are her results

Calculate an estimate for the mean

Weight 61 – 65 66 – 70 71 – 75 76 –80 81 - 85

Freq. 9 20 29 15 7

First of all we need a representative value for each group

Weight 61 – 65 66 – 70 71 – 75 76 –80 81 - 85

Freq. 9 20 29 15 7

63 68 73 78 83Mid-point

=

m 63 68 73 78 83

Weight 61 – 65 66 – 70 71 – 75 76 –80 81 - 85

Freq. 9 20 29 15 7

m x f

f

mfMean =

80

5795= 72.4375 = 72.4 (3 sf)

Now we need to calculate a total of the weight of tomatoes in each group

63 x 9567 68 x 201360 73 x 29 78 x 15 83 x 72117 1170 581

80

5795

We need to work out the total of our estimate of the weightand the total frequency

Why is this an estimate of the mean?

Because the data has been grouped and so exact data has been lost

Calculate an estimate of the mean for this distribution

Weight (Kg)

0-10 10-20 20-30 30-40 40-50 50-60

Frequency 11 18 16 11 5 2

Wt (Kg)

0-10 10-20 20-30 30-40 40-50 50-60

F 11 18 16 11 5 2

5 15 25 35 45Mid-point 55

63

14455 x 11 15 x 18 25 x 16 35 x 11 45 x 5 55 x 255 270 400 385 225 110

f

mfMean =

63

1445= 22.9365.. = 22.9 (3 sf)

m x f