R S Aggarwal and Veena Aggarwal Solutions for Exercise 6: Exercise 18F

The following table gives the production yield per hectare of wheat of $100$ farms of a village.

$\begin{array}{|ccccccc|}\hline \begin{array}{c}\text{ Production }\\ \text{ yield }\\ \text{ (kg/ha) }\end{array}& 50-55& 55-60& 60-65& 65-70& 70-75& 75-80\\ \begin{array}{c}\text{ Number of }\\ \text{ farms }\end{array}& 2& 8& 12& 24& 38& 16\\ \hline\end{array}$

Change the distribution to a 'more than type' distribution and draw its ogive. Using ogive, find the median of the given data.

The table given below shows the weekly expenditures on food of some households in a locality.

$\begin{array}{|cc|}\hline \mathrm{Weekly}\mathrm{expenditure}(\mathrm{in} \mathrm{Rs}.)& \mathrm{Number}\mathrm{of}households\\ 100-200& 5\\ 200-300& 6\\ 300-400& 11\\ 400-500& 13\\ 500-600& 5\\ 600-700& 4\\ 700-800& 3\\ 800-900& 2\\ \hline\end{array}$

Draw a 'less than type' and a 'more than type' ogive for this distribution.

From the following frequency distribution, prepare the 'more than' ogive.

$\begin{array}{|cc|}\hline \mathrm{Score}& \mathrm{No}. \mathrm{of} candidates\\ 400-450& 20\\ 450-500& 35\\ 500-550& 40\\ 550-600& 32\\ 600-650& 24\\ 650-700& 27\\ 700-750& 18\\ 750-800& 34\\ \mathrm{Total}& 230\\ \hline\end{array}$

Also find the median.

Find the mode of the given data:

$\begin{array}{|ccccc|}\hline \mathrm{Class}interval& 0-20& 20-40& 40-60& 60-80\\ \mathrm{Frequency}& 15& 6& 18& 10\\ \hline\end{array}$

In the following data, find the values of $p$ and $q$. Also, find the median class and modal class.

$\begin{array}{|ccc|}\hline \mathrm{Class}& \mathrm{Frequency}\left(\mathrm{f}\right)& \begin{array}{c}\mathrm{Cumulative}frequency\\ \left(\mathrm{cf}\right)\end{array}\\ 100-200& 11& 11\\ 200-300& 12& \mathrm{p}\\ 300-400& 10& 33\\ 400-500& \mathrm{q}& 46\\ 500-600& 20& 66\\ 600-700& 14& 80\\ \hline\end{array}$

The following frequency distribution gives the monthly consumption of electricity of $64$ consumers of a locality.

$\begin{array}{|ccccccc|}\hline \begin{array}{c}\mathrm{Monthly}\\ \mathrm{consumption}\\ (\mathrm{in}units)\end{array}& 65-85& 85-105& 105-125& 125-145& 145-165& 165-185\\ \mathrm{Number} \mathrm{of} \mathrm{consumers}& 4& 5& 13& 20& 14& 8\\ \hline\end{array}$

Form a 'more than type' cumulative frequency distribution.