Question

The weights (in grams) of 40 bananas picked at random from a basket are as follows:

84, 45, 30, 110, 75, 100, 40, 70, 60, 70, 75, 40, 100, 65, 60, 95, 85, 80, 70, 45, 35, 30, 55, 70, 110, 80, 75, 85, 70, 85, 75, 90, 30, 100, 55, 45, 65, 60, 50, 40.

Construct a cumulative frequency distribution table.

Answer 1

Given:

The weights (grams) of 40 bananas are:

84, 45, 30, 110, 75, 100, 40, 70, 60, 70, 75, 40, 100, 65, 60, 95, 85, 80, 70, 45, 35, 30, 55, 70, 110, 80, 75, 85, 70, 85, 75, 90, 30, 100, 55, 45, 65, 60, 50, 40

Step-wise calculation:

1. Choose equal class intervals of width 10 covering the data range (min = 30, max = 110):

30 – 39, 40 – 49, 50 – 59, 60 – 69, 70 – 79, 80 – 89, 90 – 99, 100 – 109, 110 – 119

2. Count frequencies in each class (tally from the list):

30 – 39 : Frequency = 4

40 – 49 : Frequency = 6

50 – 59 : Frequency = 3

60 – 69 : Frequency = 5

70 – 79 : Frequency = 9

80 – 89 : Frequency = 6

90 – 99 : Frequency = 2

100 – 109 : Frequency = 3

110 – 119 : Frequency = 2

3. Form cumulative frequencies (running totals from lowest class upward):

≤ 39 : 4

≤ 49 : 4 + 6 = 10

≤ 59 : 10 + 3 = 13

≤ 69 : 13 + 5 = 18

≤ 79 : 18 + 9 = 27

≤ 89 : 27 + 6 = 33

≤ 99 : 33 + 2 = 35

≤ 109 : 35 + 3 = 38

≤ 119 : 38 + 2 = 40

Cumulative frequency distribution table:

Class interval	Frequency	Cumulative frequency
30 – 39	4	4
40 – 49	6	10
50 – 59	3	13
60 – 69	5	18
70 – 79	9	27
80 – 89	6	33
90 – 99	2	35
100 – 109	3	38
110 – 119	2	40
Total	N = 40