Q. 2.68 - 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 cutpoint grouping with a first class 10-under 15.

Step-by-Step Solution

Answer

Part a. The frequency distribution is given as  

Class	Tally	Frequency
10-under 15	||||	4
15-under 20	|||||	5
20-under 25	|||||||	7
25-under 30	|||	3
30-under 35	-	0
35-under 40	|	1

Part b. The relative frequency distribution is given as   

Class	Frequency	Relative Frequency
10-under 15	4	$\frac{4}{20}=0.2$
15-under 20	5	$\frac{5}{20}=0.25$
20-under 25	7	$\frac{7}{20}=0.35$
25-under 30	3	$\frac{3}{20}=0.15$
30-under 35	0	0
35-under 40	1	$\frac{1}{20}=0.05$
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 the cutpoint grouping with a first class 10-under 15 the frequency distribution is given as

Class	Tally	Frequency
10-under 15	||||	4
15-under 20	|||||	5
20-under 25	|||||||	7
25-under 30	|||	3
30-under 35	-	0
35-under 40	|	1

Part (b) Step 1. Relative frequency distribution

The relative frequency distribution for the given data is given as

Class	Frequency	Relative Frequency
10-under 15	4	$\frac{4}{20}=0.2$
15-under 20	5	$\frac{5}{20}=0.25$
20-under 25	7	$\frac{7}{20}=0.35$
25-under 30	3	$\frac{3}{20}=0.15$
30-under 35	0	0
35-under 40	1	$\frac{1}{20}=0.05$
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