Question

1. the data set is the number of minutes a sample of 25 people exercise each week. 108 139 120 123 120 132 123 131 131 157 150 124 111 101 135 119 116 117 127 128 139 119 118 114 127 a. make a frequency distribution of the data set using five classes. include class limits, midpoints, frequencies, boundaries, relative frequencies, and cumulative frequencies. b. display the data using the following: b1. frequency histogram

Explanation:

Step1: Calculate class midpoints

Midpoint formula: $\text{Midpoint}=\frac{\text{Lower class limit}+\text{Upper class limit}}{2}$
For class $101 - 112$: $\frac{101 + 112}{2}=106.5$
For class $113 - 124$: $\frac{113+124}{2}=118.5$
For class $125 - 136$: $\frac{125 + 136}{2}=130.5$
For class $137 - 148$: $\frac{137+148}{2}=142.5$
For class $149 - 160$: $\frac{149+160}{2}=154.5$

Step2: Calculate class boundaries

Subtract $0.5$ from lower class limit and add $0.5$ to upper class limit.
For class $101 - 112$: $100.5 - 112.5$
For class $113 - 124$: $112.5 - 124.5$
For class $125 - 136$: $124.5 - 136.5$
For class $137 - 148$: $136.5 - 148.5$
For class $149 - 160$: $148.5 - 160.5$

Step3: Calculate relative frequencies

Relative frequency formula: $\text{Relative frequency}=\frac{\text{Frequency}}{\text{Total frequency}}$
Total frequency $n = 25$
For class $101 - 112$: $\frac{3}{25}=0.12$
For class $113 - 124$: $\frac{11}{25}=0.44$
For class $125 - 136$: $\frac{7}{25}=0.28$
For class $137 - 148$: $\frac{2}{25}=0.08$
For class $149 - 160$: $\frac{2}{25}=0.08$

Step4: Calculate cumulative frequencies

Cumulative frequency starts from the first class.
For class $101 - 112$: $3$
For class $113 - 124$: $3 + 11=14$
For class $125 - 136$: $14+7 = 21$
For class $137 - 148$: $21+2=23$
For class $149 - 160$: $23+2=25$

Answer:

Class	Midpoint	Boundaries	Relative Frequency	Cumulative Frequency
$113 - 124$	$118.5$	$112.5 - 124.5$	$0.44$	$14$
$125 - 136$	$130.5$	$124.5 - 136.5$	$0.28$	$21$
$137 - 148$	$142.5$	$136.5 - 148.5$	$0.08$	$23$
$149 - 160$	$154.5$	$148.5 - 160.5$	$0.08$	$25$