EXERCISE 13.2 — NCERT Solutions for Class 10 Mathematics Chapter 13

EXERCISE 13.2 1–6 (part 2 of 3)

Exercise 1

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

Age (in years)	$\displaystyle 5$ - $\displaystyle 15$	$\displaystyle 15$ - $\displaystyle 25$	$\displaystyle 25$ - $\displaystyle 35$	$\displaystyle 35$ - $\displaystyle 45$	$\displaystyle 45$ - $\displaystyle 55$	$\displaystyle 55$ - $\displaystyle 65$
Number of patients	$\displaystyle 6$	$\displaystyle 11$	$\displaystyle 21$	$\displaystyle 23$	$\displaystyle 14$	$\displaystyle 5$

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

NCERT’s answer

Mode $\displaystyle =36.8$ years, Mean $\displaystyle =35.37$ years. Maximum number of patients admitted in the hospital are of the age $\displaystyle 36.8$ years (approx.), while on an average the age of a patient admitted to the hospital is $\displaystyle 35.37$ years.

Working being prepared

Exercise 2

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

\displaystyle 225

electrical components :

Lifetimes (in hours)	$\displaystyle 0$ - $\displaystyle 20$	$\displaystyle 20$ - $\displaystyle 40$	$\displaystyle 40$ - $\displaystyle 60$	$\displaystyle 60$ - $\displaystyle 80$	$\displaystyle 80$ - $\displaystyle 100$	$\displaystyle 100$ - $\displaystyle 120$
Frequency	$\displaystyle 10$	$\displaystyle 35$	$\displaystyle 52$	$\displaystyle 61$	$\displaystyle 38$	$\displaystyle 29$

Determine the modal lifetimes of the components.

NCERT’s answer

65.$\displaystyle 625$ hours

Working being prepared

Exercise 3

The following data gives the distribution of total monthly household expenditure of

\displaystyle 200

families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure :

Expenditure (in ₹)	Number of families
$\displaystyle 1000$ - $\displaystyle 1500$	$\displaystyle 24$
$\displaystyle 1500$ - $\displaystyle 2000$	$\displaystyle 40$
$\displaystyle 2000$ - $\displaystyle 2500$	$\displaystyle 33$
$\displaystyle 2500$ - $\displaystyle 3000$	$\displaystyle 28$
$\displaystyle 3000$ - $\displaystyle 3500$	$\displaystyle 30$
$\displaystyle 3500$ - $\displaystyle 4000$	$\displaystyle 22$
$\displaystyle 4000$ - $\displaystyle 4500$	$\displaystyle 16$
$\displaystyle 4500$ - $\displaystyle 5000$	$\displaystyle 7$

NCERT’s answer

Modal monthly expenditure $\displaystyle =₹ 1847.83$, Mean monthly expenditure $\displaystyle =₹ 2662.5$.

Working being prepared

Exercise 4

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.

Number of students per teacher	Number of states / U.T.
$\displaystyle 15$ - $\displaystyle 20$	$\displaystyle 3$
$\displaystyle 20$ - $\displaystyle 25$	$\displaystyle 8$
$\displaystyle 25$ - $\displaystyle 30$	$\displaystyle 9$
$\displaystyle 30$ - $\displaystyle 35$	$\displaystyle 10$
$\displaystyle 35$ - $\displaystyle 40$	$\displaystyle 3$
$\displaystyle 40$ - $\displaystyle 45$	$\displaystyle 0$
$\displaystyle 45$ - $\displaystyle 50$	$\displaystyle 0$
$\displaystyle 50$ - $\displaystyle 55$	$\displaystyle 2$

NCERT’s answer

Mode : $\displaystyle 30.6$, Mean = 29.2. Most states/U.T. have a student teacher ratio of $\displaystyle 30.6$ and on an average, this ratio is 29.2.

Working being prepared

Exercise 5

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

Runs scored	Number of batsmen
$\displaystyle 3000$ - $\displaystyle 4000$	$\displaystyle 4$
$\displaystyle 4000$ - $\displaystyle 5000$	$\displaystyle 18$
$\displaystyle 5000$ - $\displaystyle 6000$	$\displaystyle 9$
$\displaystyle 6000$ - $\displaystyle 7000$	$\displaystyle 7$
$\displaystyle 7000$ - $\displaystyle 8000$	$\displaystyle 6$
$\displaystyle 8000$ - $\displaystyle 9000$	$\displaystyle 3$
$\displaystyle 9000$ - $\displaystyle 10000$	$\displaystyle 1$
$\displaystyle 10000$ - $\displaystyle 11000$	$\displaystyle 1$

Find the mode of the data.

NCERT’s answer

Mode $\displaystyle =4608.7$ runs

Working being prepared

Exercise 6

A student noted the number of cars passing through a spot on a road for

\displaystyle 100

periods each of

\displaystyle 3

minutes and summarised it in the table given below. Find the mode of the data :

Number of cars	$\displaystyle 0$ - $\displaystyle 10$	$\displaystyle 10$ - $\displaystyle 20$	$\displaystyle 20$ - $\displaystyle 30$	$\displaystyle 30$ - $\displaystyle 40$	$\displaystyle 40$ - $\displaystyle 50$	$\displaystyle 50$ - $\displaystyle 60$	$\displaystyle 60$ - $\displaystyle 70$	$\displaystyle 70$ - $\displaystyle 80$
Frequency	$\displaystyle 7$	$\displaystyle 14$	$\displaystyle 13$	$\displaystyle 12$	$\displaystyle 20$	$\displaystyle 11$	$\displaystyle 15$	$\displaystyle 8$

NCERT’s answer

Mode $\displaystyle =44.7 \mathrm{cars}$

Working being prepared