Question

A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature as follows: 58,61,63,64,66,67,68,69,70,75, 76,77,77,78,79,81,82,86,85,87,88,92,93,94,99. Use as a first class 58 – 63.

a.	Construct a relative frequency distribution.
b.	Construct a cumulative frequency distribution.
c.	Construct a cumulative relative frequency distribution.

Answer 1

The frequency, Relative frequency, Cumulative frequency distribution, and the cumulative relative frequency distribution is tabulated as:

Class	Frequency	Relative Frequency	Cumulative relative frequency	Cumulative frequency
58-63	3	0.12	0.12	3
64-69	5	0.2	0.32	8
70-75	2	0.08	0.4	10
76-81	6	0.24	0.64	16
82-87	4	0.16	0.8	20
88-93	3	0.12	0.92	23
94-99	2	0.08	1	25

=> The frequency is the no if element or values occurring in the given class.

=> The Relative frequency is the value of a class is the relative value of the frequency with respect to the total no of values, it is calculated as the class frequency / Total frequency.

=> The Cumulative relative frequency is the running sum of the relative frequency, it is calculated as the sum of => current class relative frequency and the sum of all previous class relative frequencies.

=> The Cumulative frequency is the running sum of the frequency, it is calculated as the sum of current class frequency and the sum of all previous class relative frequencies.