Q. 2.67 - 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 $50-59$ and a class width of $10$.

Step-by-Step Solution

Answer

Part a. The frequency distribution is given as  

Class	Tally	Frequency
50-59	||||||	6
60-69	|||	3
70-79	||||||	6
80-89	|||||||	7
90-99	|||	3

Part b. The relative frequency distribution is given as 

Class	Frequency	Relative Frequency
50-59	6	$\frac{6}{25}=0.24$
60-69	3	$\frac{3}{25}=0.12$
70-79	6	$\frac{6}{25}=0.24$
80-89	7	$\frac{7}{25}=0.28$
90-99	3	$\frac{3}{25}=0.12$
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 $50-59$ and a class width of $10$, the frequency distribution can be given as

Class	Tally	Frequency
50-59	||||||	6
60-69	|||	3
70-79	||||||	6
80-89	|||||||	7
90-99	|||	3

Part (b) Step 1. Relative frequency distribution

The relative frequency distribution for the given data is given as

Class	Frequency	Relative Frequency
50-59	6	$\frac{6}{25}=0.24$
60-69	3	$\frac{3}{25}=0.12$
70-79	6	$\frac{6}{25}=0.24$
80-89	7	$\frac{7}{25}=0.28$
90-99	3	$\frac{3}{25}=0.12$
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