Question

The following is the distribution of weights (in $\mathrm{kg}$) of $40$ persons : Weight (in $\mathrm{kg}$)

$40-45,45-50,50-55,55-60,60-65,65-70,70-75,75-80$.

Number of persons $4,4,13,5,6,5,2,1$

Construct a cumulative frequency distribution (of the less than type) table for the data above.

Answer 1

Less than cumulative frequency distribution:

The less than cumulative frequency distribution is obtained by adding successively the frequencies of all the previous classes along with the class

against which it is written. In this type, the cumulate begins from the lowest to the highest size.

The data represents the weight of $40$ persons.

We have to construct a cumulative frequency distribution of the less than type table for the data.

C.I	Fi	Weight ( in kg )	Cumulative frequency
$$\begin{gathered} 40-45 \\ 45-50 \\ 50-55 \\ 55-60 \\ 60-65 \\ 65-70 \\ 70-75 \\ 75-80 \end{gathered}$$	$$\begin{gathered} 4 \\ 4 \\ 13 \\ 5 \\ 6 \\ 5 \\ 2 \\ 1 \end{gathered}$$	$$\begin{gathered} \mathrm{Less}\mathrm{than}45 \\ \mathrm{Lesss}\mathrm{than}50 \\ \mathrm{Lesss}\mathrm{than}55 \\ \mathrm{Lesss}\mathrm{than}60 \\ \mathrm{Lesss}\mathrm{than}65 \\ \mathrm{Lesss}\mathrm{than}70 \\ \mathrm{Lesss}\mathrm{than}75 \\ \mathrm{Lesss}\mathrm{than}80 \end{gathered}$$	$$\begin{gathered} 00+04=04 \\ 04+04=08 \\ 08+13=21 \\ 21+05=26 \\ 26+06=32 \\ 32+05=37 \\ 37+02=39 \\ 39+01=40 \end{gathered}$$

Hence, the data's cumulative frequency distribution (of the less than type) table is shown above.