Question

frequency table of grouped data
the following raw data consists of the weights, in pounds, of 30 high school students:
106 108 110 112 113 113 115 117 120 121
126 135 142 148 150 155 160 168 170 182
185 195 195 200 206 206 209 210 212 223
class width = 10
16 - 26) using the data, complete the frequency distribution table below. (5points)
class intervals (in pounds) frequency class boundaries class midpoint cumulative frequency
106 - 115 8 115.5
116 - 125 4 125.5
126 - 135 2 135.5
136 - 145 2 145.5
146 - 155 2 155.5
156 - 165 1

Explanation:

Step1: Calculate class mid - point formula

The formula for the class mid - point is $\text{Mid - point}=\frac{\text{Lower limit}+\text{Upper limit}}{2}$.

Step2: Calculate mid - points for each class interval

For the class interval $106 - 115$: $\text{Mid - point}=\frac{106 + 115}{2}=\frac{221}{2}=110.5$
For the class interval $116 - 125$: $\text{Mid - point}=\frac{116+125}{2}=\frac{241}{2}=120.5$
For the class interval $126 - 135$: $\text{Mid - point}=\frac{126 + 135}{2}=\frac{261}{2}=130.5$
For the class interval $136 - 145$: $\text{Mid - point}=\frac{136+145}{2}=\frac{281}{2}=140.5$
For the class interval $146 - 155$: $\text{Mid - point}=\frac{146 + 155}{2}=\frac{301}{2}=150.5$
For the class interval $156 - 165$: $\text{Mid - point}=\frac{156+165}{2}=\frac{321}{2}=160.5$

Step3: Calculate cumulative frequency

The cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.
For the first class $106 - 115$ with frequency $8$, the cumulative frequency is $8$.
For the second class $116 - 125$ with frequency $4$, the cumulative frequency is $8 + 4=12$.
For the third class $126 - 135$ with frequency $2$, the cumulative frequency is $12+2 = 14$.
For the fourth class $136 - 145$ with frequency $2$, the cumulative frequency is $14 + 2=16$.
For the fifth class $146 - 155$ with frequency $2$, the cumulative frequency is $16+2 = 18$.
For the sixth class $156 - 165$ with frequency $1$, the cumulative frequency is $18+1=19$.

Answer:

Class Intervals (in pounds)	Frequency	Class Boundaries	Class Midpoint	Cumulative Frequency
$116 - 125$	$4$	-	$120.5$	$12$
$126 - 135$	$2$	-	$130.5$	$14$
$136 - 145$	$2$	-	$140.5$	$16$
$146 - 155$	$2$	-	$150.5$	$18$
$156 - 165$	$1$	-	$160.5$	$19$