Question

Construct the cumulative frequency distribution that corresponds to the given frequency distribution. Height (inches) Frequency 69.0 719 72.0-749 75.0-77.9 78.0-80.9 81.0-83.9 21 16 19 Height Cumulative (inches) Frequency less than 72.0 less than 75.0 less than 78.0 less than 81.0 s 83.9 0.263 0.200 0.237 0.275 0.025 Height Cumulative (inches) Frequency less than 720 less than 75.0 less than 780 less than 81.0 s 83.9 37 56 78 80 82 Height Cumulative (inches) Frequency less than 72.0 less than 75.0 less than 78.0 less than 81.0 s 83.9 21 37 56 78 80

Answer 1

Here given frequency table is as

Height(Inches)	Frequency
69.0 - 71.9	21
72.0 - 74.9	16
75.0 - 77.9	19
78.0 - 80.9	22
81.0 - 83.9	2

We construct the cumulative frequency table using following formula.

Here, i = 1, 2, 3, 4, 5 classes. Therefore

1^st cumulative = o^th observation + 1^st observation = 0 + 21 = 21

2^nd cumulative = 1^st cumulative + 2^nd observation = 21 + 16 = 37

3^rd cumulative = 2^nd cumulative + 3^rd observation = 37 + 19 = 56

4^th cumulative = 3^rd cumulative + 4^th observation = 56 + 22 = 78

5^th cumulative = 4^th cumulative + 5^th observation = 78 + 2 = 80

So cumulative frequency table is as

Height (Inches)	Cumulative Frequency
Less Than 71.9	21
Less Than 74.9	37
Less Than 77.9	56
Less Than 80.9	78
<= 83.9	80