NCERT Solutions · Class 10 Mathematics Statistics

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in $\displaystyle 20$ houses in a locality. Find the mean number of plants per house.

Number of plants	$\displaystyle 0$-$\displaystyle 2$	$\displaystyle 2$-$\displaystyle 4$	$\displaystyle 4$-$\displaystyle 6$	$\displaystyle 6$-$\displaystyle 8$	$\displaystyle 8$-$\displaystyle 10$	$\displaystyle 10$-$\displaystyle 12$	$\displaystyle 12$-$\displaystyle 14$
Number of houses	$\displaystyle 1$	$\displaystyle 2$	$\displaystyle 1$	$\displaystyle 5$	$\displaystyle 6$	$\displaystyle 2$	$\displaystyle 3$

Which method did you use for finding the mean, and why?

Consider the following distribution of daily wages of $\displaystyle 50$ workers of a factory.

Daily wages (in ₹)	$\displaystyle 500$-$\displaystyle 520$	$\displaystyle 520$-$\displaystyle 540$	$\displaystyle 540$-$\displaystyle 560$	$\displaystyle 560$-$\displaystyle 580$	$\displaystyle 580$-$\displaystyle 600$
Number of workers	$\displaystyle 12$	$\displaystyle 14$	$\displaystyle 8$	$\displaystyle 6$	$\displaystyle 10$

Find the mean daily wages of the workers of the factory by using an appropriate method.

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency $\displaystyle f$.

Daily pocket allowance (in ₹)	$\displaystyle 11$-$\displaystyle 13$	$\displaystyle 13$-$\displaystyle 15$	$\displaystyle 15$-$\displaystyle 17$	$\displaystyle 17$-$\displaystyle 19$	$\displaystyle 19$-$\displaystyle 21$	$\displaystyle 21$-$\displaystyle 23$	$\displaystyle 23$-$\displaystyle 25$
Number of children	$\displaystyle 7$	$\displaystyle 6$	$\displaystyle 9$	$\displaystyle 13$	$\displaystyle f$	$\displaystyle 5$	$\displaystyle 4$

Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.

Number of heartbeats per minute	$\displaystyle 65$-$\displaystyle 68$	$\displaystyle 68$-$\displaystyle 71$	$\displaystyle 71$-$\displaystyle 74$	$\displaystyle 74$-$\displaystyle 77$	$\displaystyle 77$-$\displaystyle 80$	$\displaystyle 80$-$\displaystyle 83$	$\displaystyle 83$-$\displaystyle 86$
Number of women	$\displaystyle 2$	$\displaystyle 4$	$\displaystyle 3$	$\displaystyle 8$	$\displaystyle 7$	$\displaystyle 4$	$\displaystyle 2$

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes	$\displaystyle 50$-$\displaystyle 52$	$\displaystyle 53$-$\displaystyle 55$	$\displaystyle 56$-$\displaystyle 58$	$\displaystyle 59$-$\displaystyle 61$	$\displaystyle 62$-$\displaystyle 64$
Number of boxes	$\displaystyle 15$	$\displaystyle 110$	$\displaystyle 135$	$\displaystyle 115$	$\displaystyle 25$

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

The table below shows the daily expenditure on food of $\displaystyle 25$ households in a locality.

Daily expenditure (in ₹)	$\displaystyle 100$-$\displaystyle 150$	$\displaystyle 150$-$\displaystyle 200$	$\displaystyle 200$-$\displaystyle 250$	$\displaystyle 250$-$\displaystyle 300$	$\displaystyle 300$-$\displaystyle 350$
Number of households	$\displaystyle 4$	$\displaystyle 5$	$\displaystyle 12$	$\displaystyle 2$	$\displaystyle 2$

Find the mean daily expenditure on food by a suitable method.

To find out the concentration of $\displaystyle \mathrm{SO}_{2}$ in the air (in parts per million, i.e., ppm), the data was collected for $\displaystyle 30$ localities in a certain city and is presented below:

Concentration of $\displaystyle \mathbf{S O}_{\mathbf{2}}$ (in ppm)	Frequency
$\displaystyle 0.00$-$\displaystyle 0.04$	$\displaystyle 4$
$\displaystyle 0.04$-$\displaystyle 0.08$	$\displaystyle 9$
$\displaystyle 0.08$-$\displaystyle 0.12$	$\displaystyle 9$
$\displaystyle 0.12$-$\displaystyle 0.16$	$\displaystyle 2$
$\displaystyle 0.16$-$\displaystyle 0.20$	$\displaystyle 4$
$\displaystyle 0.20$-$\displaystyle 0.24$	$\displaystyle 2$

Find the mean concentration of $\displaystyle \mathrm{SO}_{2}$ in the air.

A class teacher has the following absentee record of $\displaystyle 40$ students of a class for the whole term. Find the mean number of days a student was absent.

Number of days	$\displaystyle 0$-$\displaystyle 6$	$\displaystyle 6$-$\displaystyle 10$	$\displaystyle 10$-$\displaystyle 14$	$\displaystyle 14$-$\displaystyle 20$	$\displaystyle 20$-$\displaystyle 28$	$\displaystyle 28$-$\displaystyle 38$	$\displaystyle 38$-$\displaystyle 40$
Number of students	$\displaystyle 11$	$\displaystyle 10$	$\displaystyle 7$	$\displaystyle 4$	$\displaystyle 4$	$\displaystyle 3$	$\displaystyle 1$

The following table gives the literacy rate (in percentage) of $\displaystyle 35$ cities. Find the mean literacy rate.

Literacy rate (in \%)	$\displaystyle 45$-$\displaystyle 55$	$\displaystyle 55$-$\displaystyle 65$	$\displaystyle 65$-$\displaystyle 75$	$\displaystyle 75$-$\displaystyle 85$	$\displaystyle 85$-$\displaystyle 95$
Number of cities	$\displaystyle 3$	$\displaystyle 10$	$\displaystyle 11$	$\displaystyle 8$	$\displaystyle 3$