Q. 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.

No. of mangoes	$50-52$	$53-55$	$56-58$	$59-61$	$62-64$
No. of boxes	$15$	$110$	$135$	$115$	$25$

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

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

Daily pocket Allowance (in Rs.)	Number of children
11-13	7
13-15	6
15-17	9
17-19	13
19-21	f
21-23	5
23-25	4

1. $f=10$
2. $f=20$
3. $f=15$
4. $f=19$

Q. To find out the concentration of $S{O}_2$ in the air (in parts per million, i.e., ppm), the data was collected for $30$ localities in a certain city and is presented below:

Concentration of $S{O}_2$ (in ppm)	Frequency
$0.00-0.04$	$4$
$0.04-0.08$	$9$
$0.08-0.12$	$9$
$0.12-0.16$	$2$
$0.16-0.20$	$4$
$0.20-0.24$	$2$

Find the mean concentration of $S{O}_2$ in the air.

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

Daily expenditure (in Rs.)	100-150	150-200	200-250	250-300	300-350
Number of households:	$4$	$5$	$12$	$2$	$2$

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

Q. Consider the following distribution of daily wages of 50 workers of a factory:
Find the mean daily wages of the workers of the factory by using appropriate method.

Daily wages(in rs)	Number of workers
500-200	12
520-540	14
540-560	8
560-580	6
580-600	10

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

Literacy rate (in $\%$)	$45-55$	$55-65$	$65-75$	$75-85$	$85-95$
No. of cities	$3$	$10$	$11$	$8$	$3$

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

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

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

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

Q. 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 $20$ houses in a locality.Find the mean number of plants per house.

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

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

Q. A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:

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

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

Age (in years)	No. of patients
5-15	6
15-25	11
25-35	21
35-45	23
45-55	14
55-65	5

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

Q. 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.
$15-20$	$3$
$20-25$	$8$
$25-30$	$9$
$30-35$	$10$
$35-40$	$3$
$40-45$	$0$
$45-50$	$0$
$50-55$	$2$

Q. 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
$3000-4000$	$4$
$4000-5000$	$18$
$5000-6000$	$9$
$6000-7000$	$7$
$7000-8000$	$6$
$8000-9000$	$3$
$9000-10000$	$1$
$10000-11000$	$1$

Find the mode of the data.

Q. 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:

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

Q. The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components:

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

Determine the modal lifetimes of the components.

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

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

Q. The following table gives the distribution of the life time of 400 neon lamps:

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

Find the median life time of a lamp.

Q.

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

$\begin{array}{cccccccc}\text{Weight(in Kgs)}& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70& 70-75\\ \text{Number of students}& 2& 3& 8& 6& 6& 3& 2\end{array}$

Q. The lengths of $40$ 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
$118-126$ $127-135$ $136-144$ $145-153$ $154-162$ $163-171$ $172-180$	$3$ $5$ $9$ $12$ $5$ $4$ $2$

Find the median length of the leaves.

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

Age (in years)	No. of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

1. $62.12$ years
2. $53.53$ years
3. None of these
4. $35.76$ years