Q. 2.65 - Elementary Statistics

Question

In Exercises 2.60-2.71. we have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set,

a. determine a frequency distribution 

b. obtain a relative-frequency distribution.

c. construct a frequency histogram based on your result from part (a).

d. construct a relative-frequency histogram based on your result

from part (b).

Use limit grouping with a first class of $0-4$ and a class width of $5$.

Step-by-Step Solution

Answer

Part a. The frequency distribution is given as  

Class	Tally	Frequency
0-4	|||||	5
5-9	|||||	5
10-14	|	1
15-19	||||	4
20-24	||	2
25-29	|||	3

Part b. The relative frequency distribution is given as 

Class	Frequency	Relative Frequency
0-4	5	$\frac{5}{20}=0.25$
5-9	5	$\frac{5}{20}=0.25$
10-14	1	$\frac{1}{20}=0.05$
15-19	4	$\frac{4}{20}=0.2$
20-24	2	$\frac{2}{20}=0.1$
25-29	3	$\frac{3}{20}=0.15$
Total	20	1

Part c. The frequency histogram is given as 

Part d. The relative frequency histogram is given as   

Part (a) Step 1. Given Information

We are given a quantitative data set.

Part (a) Step 2. Frequency Distribution

Using limit grouping with a first class of $0-4$ and a class width of $5$, the frequency distribution can be given as

Class	Tally	Frequency
0-4	|||||	5
5-9	|||||	5
10-14	|	1
15-19	||||	4
20-24	||	2
25-29	|||	3

Part (b) Step 1. Relative frequency distribution

The relative frequency distribution for the given data is given as

Class	Frequency	Relative Frequency
0-4	5	$\frac{5}{20}=0.25$
5-9	5	$\frac{5}{20}=0.25$
10-14	1	$\frac{1}{20}=0.05$
15-19	4	$\frac{4}{20}=0.2$
20-24	2	$\frac{2}{20}=0.1$
25-29	3	$\frac{3}{20}=0.15$
Total	20	1

Part (c) Step 1. Frequency histogram

The frequency histogram for the frequency distribution can be given as

Part (d) Step 1. Relative frequency histogram

The relative-frequency histogram for the relative-frequency distribution can be given as