NCERT Solutions · Class 10 Mathematics Statistics

The following frequency distribution gives the monthly consumption of electricity of $\displaystyle 68$ consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption (in units)	Number of consumers
$\displaystyle 65$-$\displaystyle 85$	$\displaystyle 4$
$\displaystyle 85$-$\displaystyle 105$	$\displaystyle 5$
$\displaystyle 105$-$\displaystyle 125$	$\displaystyle 13$
$\displaystyle 125$-$\displaystyle 145$	$\displaystyle 20$
$\displaystyle 145$-$\displaystyle 165$	$\displaystyle 14$
$\displaystyle 165$-$\displaystyle 185$	$\displaystyle 8$
$\displaystyle 185$-$\displaystyle 205$	$\displaystyle 4$

If the median of the distribution given below is $\displaystyle 28.5$, find the values of $\displaystyle x$ and $\displaystyle y$.

Class interval	Frequency
$\displaystyle 0$-$\displaystyle 10$	$\displaystyle 5$
$\displaystyle 10$-$\displaystyle 20$	$\displaystyle x$
$\displaystyle 20$-$\displaystyle 30$	$\displaystyle 20$
$\displaystyle 30$-$\displaystyle 40$	$\displaystyle 15$
$\displaystyle 40$-$\displaystyle 50$	$\displaystyle y$
$\displaystyle 50$-$\displaystyle 60$	$\displaystyle 5$
Total	$\displaystyle 60$

A life insurance agent found the following data for distribution of ages of $\displaystyle 100$ policy holders. Calculate the median age, if policies are given only to persons having age $\displaystyle 18$ years onwards but less than $\displaystyle 60$ year.

Age (in years)	Number of policy holders
Below $\displaystyle 20$	$\displaystyle 2$
Below $\displaystyle 25$	$\displaystyle 6$
Below $\displaystyle 30$	$\displaystyle 24$
Below $\displaystyle 35$	$\displaystyle 45$
Below $\displaystyle 40$	$\displaystyle 78$
Below $\displaystyle 45$	$\displaystyle 89$
Below $\displaystyle 50$	$\displaystyle 92$
Below $\displaystyle 55$	$\displaystyle 98$
Below $\displaystyle 60$	$\displaystyle 100$

The lengths of $\displaystyle 40$ leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :

Length (in mm)	Number of leaves
$\displaystyle 118$-$\displaystyle 126$	$\displaystyle 3$
$\displaystyle 127$-$\displaystyle 135$	$\displaystyle 5$
$\displaystyle 136$-$\displaystyle 144$	$\displaystyle 9$
$\displaystyle 145$-$\displaystyle 153$	$\displaystyle 12$
$\displaystyle 154$-$\displaystyle 162$	$\displaystyle 5$
$\displaystyle 163$-$\displaystyle 171$	$\displaystyle 4$
$\displaystyle 172$-$\displaystyle 180$	$\displaystyle 2$

Find the median length of the leaves. (Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to $\displaystyle 117.5$-$\displaystyle 126.5$, $\displaystyle 126.5$-$\displaystyle 135.5$, ..., $\displaystyle 171.5$-180.5.)

The following table gives the distribution of the life time of $\displaystyle 400$ neon lamps :

Life time (in hours)	Number of lamps
$\displaystyle 1500$-$\displaystyle 2000$	$\displaystyle 14$
$\displaystyle 2000$-$\displaystyle 2500$	$\displaystyle 56$
$\displaystyle 2500$-$\displaystyle 3000$	$\displaystyle 60$
$\displaystyle 3000$-$\displaystyle 3500$	$\displaystyle 86$
$\displaystyle 3500$-$\displaystyle 4000$	$\displaystyle 74$
$\displaystyle 4000$-$\displaystyle 4500$	$\displaystyle 62$
$\displaystyle 4500$-$\displaystyle 5000$	$\displaystyle 48$

Find the median life time of a lamp.

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

Number of letters	$\displaystyle 1$-$\displaystyle 4$	$\displaystyle 4$-$\displaystyle 7$	$\displaystyle 7$-$\displaystyle 10$	$\displaystyle 10$-$\displaystyle 13$	$\displaystyle 13$-$\displaystyle 16$	$\displaystyle 16$-$\displaystyle 19$
Number of surnames	$\displaystyle 6$	$\displaystyle 30$	$\displaystyle 40$	$\displaystyle 16$	$\displaystyle 4$	$\displaystyle 4$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.

The distribution below gives the weights of $\displaystyle 30$ students of a class. Find the median weight of the students.

Weight (in kg)	$\displaystyle 40$-$\displaystyle 45$	$\displaystyle 45$-$\displaystyle 50$	$\displaystyle 50$-$\displaystyle 55$	$\displaystyle 55$-$\displaystyle 60$	$\displaystyle 60$-$\displaystyle 65$	$\displaystyle 65$-$\displaystyle 70$	$\displaystyle 70$-$\displaystyle 75$
Number of students	$\displaystyle 2$	$\displaystyle 3$	$\displaystyle 8$	$\displaystyle 6$	$\displaystyle 6$	$\displaystyle 3$	$\displaystyle 2$