M L Aggarwal Solutions for Chapter: Statistics, Exercise 9: Chapter Test

Find the cumulative frequency and median of the following data: 

$\begin{array}{|lccccc|}\hline \text{ Daily wages (in ₹) }& 0-50& 60-110& 120-170& 180-230& 240-290\\ \text{ Number of labourers }& 10& 15& 12& 20& 13\\ \hline\end{array}$

A survey regarding the heights (in $cm$) of $51$ girls of class $X$ of a school was conducted and the following data was obtained:

$\begin{array}{|lcccccc|}\hline \text{ Height ( in cm) }& \text{ Below }140& \text{ Below }145& \text{ Below }150& \text{ Below }155& \text{ Below }160& \text{ Below }165\\ \text{ No. of girls }& 4& 11& 29& 40& 46& 51\\ \hline\end{array}$

Find the median height.

Find the median of the following cumulative frequency distribution:

$\begin{array}{|lcccccccc|}\hline \text{ Marks below }& 10& 20& 30& 40& 50& 60& 70& 80\\ \text{ Number of students }& 15& 35& 60& 84& 96& 127& 198& 251\\ \hline\end{array}$

The median of the following data is $50$. Find the value of $p$ and $q$, if the sum of all frequencies is $90$.

$\begin{array}{|lccccccc|}\hline \text{ Marks }& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80& 80-90\\ \text{ Frequency }& p& 15& 25& 20& q& 8& 10\\ \hline\end{array}$

Find the mean, and median of the following frequency distribution of ages of $50$ children:

$\begin{array}{|lccccc|}\hline \text{ Age (in years) }& 4-6& 6-8& 8-10& 10-12& 12-14\\ \text{ Number of children }& 3& 8& 20& 12& 7\\ \hline\end{array}$

Using the data given below construct the less than type cumulative frequency table and draw the ogive. From the ogive determine the median.

$\begin{array}{|lcccccccc|}\hline \text{ Marks }& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{ No. of students }& 3& 8& 12& 14& 10& 6& 5& 2\\ \hline\end{array}$

The following table shows the distribution of the heights of a group of factory workers:

$\begin{array}{|lccccccc|}\hline \text{ Height (in cm) }& 150-155& 155-160& 160-165& 165-170& 170-175& 175-180& 180-185\\ \text{ No. of workers }& 6& 12& 18& 20& 13& 8& 6\\ \hline\end{array}$

Convert the distribution to a more than cumulative frequency distribution and draw its ogive. Hence, obtain the median height from the graph.

The weight of tea in $70$ packets are shown in the following table:

$\begin{array}{|lcccccc|}\hline \text{ Weight (in gram) }& 200-201& 201-202& 202-203& 203-204& 204-205& 205-206\\ \text{ Number of packets }& 13& 27& 18& 10& 1& 1\\ \hline\end{array}$

Draw less than type and more than type ogives for the data and use them to find the median weight.