Answer to Question #102604 in Statistics and Probability for Junaid Mahida

Question

The Quick Change Oil Company has a number of outlets. The numbers of oil changes at the Oak Street outlet in the past 20 days are as follows:
78 114 89 69 108 83 68 82 80 113
99 78 74 101 114 119 111 91 118 63
a. How many classes would you recommend?
b. What class interval would you suggest? (Round the final answer to the nearest whole number.)
c. What lower limit would you recommend for the first class?
d. Organize the information into a frequency distribution and determine the relative frequency distribution. (Round the final answers to 2 decimal places.)
Units Frequency Relative frequency
60 to under 72
72 to under 84
84 to under 96
96 to under 108
108 to under 120
Total

Answer 1

Sort the data set in ascending order

63 68 69 74 78 78 80 82 83 89 91 99 101 108 111 113 114 114 118 119

a. How many classes would you recommend?

Number of classes should be between 5 and 20. Use '' $2^{k}$ '' rule.

There are 20 groups: $2^4=16<20, 2^5=32>20.$ I would recommend 5 classes.

b. What class interval would you suggest?

Class interval

$$class\ width=w>{max-min \over k}$$

where:

max is the maximum value in a dataset

min is the minimum value in a dataset

k is the number of classes

$$w>{119-63 \over 5}=11.2$$

I would suggest $w=12.$

c. What lower limit would you recommend for the first class?

$L=61$

d. Organize the information into a frequency distribution and determine the relative frequency distribution. 

$$\begin{matrix} Class & Class &Frequency & Relative \\ limits & boundaries & & frequency \\ 61-72 & 60.5-72.5 & 3 & 0.15 \\ 73-84 & 72.5-84.5 & 6 & 0.30\\ 85-96 & 84.5-96.5 & 2 & 0.10 \\ 97-108 & 96.5-108.5 & 3 & 0.15 \\ 109-120 & 108.5-120.5 & 6 & 0.30 \end{matrix}$$

$$Total=0.15+0.30+0.10+0.15+0.30=1$$