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.

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

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

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

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