Answer to Question #153474 in Statistics and Probability for samantha

Question

The body weights (kg) of 20 pregnant mothers attending to an antenatal Clinic were reported as Follows. 55,60,62,65,70,85,60,70,56,63,65,60,60 ,59,72,80,62,70,82,62 

1.Construct the class intervals with 7 classes.

2 Find the cumulative frequency

3 Create frequency distribution table

4 find mean, mode ,median

 

Answer 1

1.

55, 56, 59, 60, 60, 60, 60, 62, 62, 62, 63, 65, 65, 70, 70, 70, 72, 80, 82, 85

Range of scores $=85-55 =30$

Number of classes $=7$

Class width $=\dfrac{30}{7}=5$

$\begin{matrix} \begin{alignedat}{2} Class \\ limits \end{alignedat} & \begin{alignedat}{2} Class\ \ \ \ \ \ \\ boundaries \end{alignedat} & Tally & Frequency \\ 53-57 & 52.5-57.5 & || & 2 \\ 58-62 & 57.5-62.5 & \cancel{|||||}\ ||| & 8 \\ 63-67 & 62.5-67.5 & ||| & 3 \\ 68-72 & 67.5 - 72.5 & |||| & 4 \\ 73-77 & 72.5-77.5 & & 0 \\ 78-82 & 77.5-82.5 & || & 2 \\ 83-87 & 82.5-87.5 & | & 1 \end{matrix}$

2.

$\begin{matrix} \begin{alignedat}{2} Class \\ limits \end{alignedat} &\begin{alignedat}{2} Frequency \\ \end{alignedat} & \begin{alignedat}{2} Cumulative \\ frequency \end{alignedat} \\ 53-57 & 2 & 2 \\ 58-62 & 8 & 10 \\ 63-67 & 3 & 13 \\ 68-72 & 4 & 17\\ 73-77 & 0 & 17\\ 78-82 & 2 & 19 \\ 83-87 & 1 & 20 \end{matrix}$

3.

$\begin{matrix} \begin{alignedat}{2} Class \\ limits \end{alignedat} & Frequency & \begin{alignedat}{2} Cumulative \\ frequency \end{alignedat} & \begin{alignedat}{2} Percentage \\ \end{alignedat} & \begin{alignedat}{2} Cumulative \\ percentage \end{alignedat} \\ 53-57 & 2 & 2 & 0.1 & 0.1 \\ 58-62 & 8 & 10 & 0.4 & 0.5 \\ 63-67 & 3 & 13 & 0.15 & 0.65 \\ 68-72 & 4 &17 & 0.2 & 0.85 \\ 73-77 & 0 & 17 & 0 & 0.85 \\ 78-82 & 2 & 19 & 0.1 & 0.95 \\ 83-87 & 1 & 20 & 0.05 & 1 \end{matrix}$

4.

$$mean=\dfrac{1}{20}(55+56+59+4(60)+3(62)+63$$

$$+2(65)+3(70)+72+80+82+85)=65.9$$

$$mode=60, \text{appeared 4 times}$$

$$median=\dfrac{62+63}{2}=62.5$$