Q. 2.66 - 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 $30-36$ and a class width of $7$.

Step-by-Step Solution

Answer

Part a. The frequency distribution is given as  

Class	Tally	Frequency
30-36	|||||||	7
37-43	|	1
44-50	|||||	5
51-57	|||||	5
58-64	|||	3
65-71	||	2
72-78	||	2

Part b. The relative frequency distribution is given as    

Class	Frequency	Relative Frequency
30-36	7	$\frac{7}{25}=0.28$
37-43	1	$\frac{1}{25}=0.04$
44-50	5	$\frac{5}{25}=0.2$
51-57	5	$\frac{5}{25}=0.2$
68-64	3	$\frac{3}{25}=0.12$
65-71	2	$\frac{2}{25}=0.08$
72-78	2	$\frac{2}{25}=0.08$
Total	25	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 $30-36$ and a class width of $7$, the frequency distribution can be given as

Class	Tally	Frequency
30-36	|||||||	7
37-43	|	1
44-50	|||||	5
51-57	|||||	5
58-64	|||	3
65-71	||	2
72-78	||	2

Part (b) Step 1. Relative frequency distribution

The relative frequency distribution for the given data is given as

Class	Frequency	Relative Frequency
30-36	7	$\frac{7}{25}=0.28$
37-43	1	$\frac{1}{25}=0.04$
44-50	5	$\frac{5}{25}=0.2$
51-57	5	$\frac{5}{25}=0.2$
58-64	3	$\frac{3}{25}=0.12$
65-71	2	$\frac{2}{25}=0.08$
71-78	2	$\frac{2}{25}=0.08$
Total	25	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