R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: EXERCISE 17B

$100$surnames were randomly picked up from a local telephone directory and frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

$\begin{array}{|cccccc|}\hline \text{ Number of letters }& 1-4& 4-6& 6-8& 8-12& 12-20\\ \text{ Number of surnames }& 6& 30& 44& 16& 4\\ \hline\end{array}$

Write the class interval in which the maximum number of surnames lie.

Draw a histogram to represent the following information:

$\begin{array}{|cccccc|}\hline \text{ Class interval }& 5-10& 10-15& 15-25& 25-45& 45-75\\ \text{ Frequency }& 6& 12& 10& 8& 18\\ \hline\end{array}$

Draw a histogram to represent the following information:

$\begin{array}{|cccccc|}\hline \text{ Marks }& 0-10& 10-30& 30-45& 45-50& 50-60\\ \begin{array}{c}\text{ Number of }\\ \text{ students }\end{array}& 8& 32& 18& 10& 6\\ \hline\end{array}$

In a study of diabetic patients in a village, the following observations were noted.

$\begin{array}{|ccccccc|}\hline \text{ Age in years }& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{ Number of patients }& 2& 5& 12& 19& 9& 4\\ \hline\end{array}$

Represent the above data by a frequency polygon.

Draw a frequency polygon for the following frequency distribution:

$\begin{array}{|ccccccc|}\hline \text{ Class interval }& 1-10& 11-20& 21-30& 31-40& 41-50& 51-60\\ \text{ Frequency }& 8& 3& 6& 12& 2& 7\\ \hline\end{array}$

The ages (in years) of $360$ patients treated in a hospital on a particular day are given below:

$\begin{array}{|ccccccc|}\hline \text{ Age in years }& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{ Number of patients }& 90& 40& 60& 20& 120& 30\\ \hline\end{array}$

Draw a histogram and a frequency polygon on the same graph to represent the above data.

Draw a histogram and the frequency polygon from the following data:

$\begin{array}{|ccccccc|}\hline \text{ Class interval }& 20-25& 25-30& 30-35& 35-40& 40-45& 45-50\\ \text{ Frequency }& 30& 24& 52& 28& 46& 10\\ \hline\end{array}$

Draw a histogram for the following data:

$\begin{array}{|ccccccc|}\hline \text{ Class interval }& 600-640& 640-680& 680-720& 720-760& 760-800& 800-840\\ \text{ Frequency }& 18& 45& 153& 288& 171& 63\\ \hline\end{array}$

Using this histogram, draw the frequency polygon on the same graph.