Exercise 13.2

The following table shows the ages of the patients admitted in a hospital during a year:

$$\begin{array}{|c|c|c|c|c|c|c|}

\hline
\text{Age (in years)} & 5 - 15 & 15 - 25 & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 \\
\hline
\text{Number of patients} & 6 & 11 & 21 & 12 & 23 & 14 & 5 \\
\hline
\end{array}$$

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

The following data gives the information on the observed lifetimes (in hours) of electrical components:

$$\begin{array}{|c|c|}

\hline
\text{Lifetime (in hours)} & \text{Frequency} \\
\hline
0\text{–}20   & 10 \\
20\text{–}40  & 35 \\
40\text{–}60  & 52 \\
60\text{–}80  & 61 \\
80\text{–}100 & 38 \\
100\text{–}120& 29 \\
\hline
\end{array}$$

Determine the modal lifetime of the components.

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

$$\begin{array}{|c|c|}

\hline
\text{Expenditure (in } \text{₹)} & \text{Number of families} \\
\hline
1000 - 1500 & 24 \\
1500 - 2000 & 40 \\
2000 - 2500 & 33 \\
2500 - 3000 & 28 \\
3000 - 3500 & 30 \\
3500 - 4000 & 22 \\
4000 - 4500 & 16 \\
4500 - 5000 & 7 \\
\hline
\end{array}$$

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

$$\begin{array}{|c|c|}

\hline
\text{Number of students per teacher} & \text{Number of states / U.T.} \\
\hline
15 - 20 & 3 \\
20 - 25 & 8 \\
25 - 30 & 9 \\
30 - 35 & 10 \\
35 - 40 & 3 \\
40 - 45 & 0 \\
45 - 50 & 0 \\
50 - 55 & 2 \\
\hline
\end{array}$$

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

$$\begin{array}{|c|c|}

\hline
\text{Runs scored} & \text{Number of batsmen} \\
\hline
4000 - 5000 & 4 \\
\hline
5000 - 6000 & 18 \\
\hline
6000 - 7000 & 9 \\
\hline
7000 - 8000 & 7 \\
\hline
8000 - 9000 & 6 \\
\hline
9000 - 10000 & 3 \\
\hline
10000 - 11000 & 1 \\
\hline
\end{array}$$

Find the mode of the data.

periods each of 3 minutes and summarised it in the table given below. Find the mode of the data : Number of cars 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80