NCERT Solution for Class 10 Mathematics Chapter 14 Statistics
Chapter Name  NCERT Solution for Class 10 Maths Chapter 14 Statistics 
Topics Covered 

Related Study 

Short Revision for Statistics
 Mean, median and mode are the three measures of central tendency.
 Class mark = (upper class limit + lower class limit)/2 .
 The mean x is computed by the following methods :
 The median for grouped data can be computed by median =
where symbols have their usual meanings.  The x  coordinate of the point of intersection of both the ogives of grouped data gives the median.
 The mode for grouped data can be obtained by mode =
where symbols have their usual meanings.  Mode = 3 median  2 mean
NCERT Exercise Solutions
Exercise 14.1
1. A survey was conducted by a group of students as a part of their environment awareness program, 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 
02 
24 
46 
68 
810 
1012 
1214 
Number of Houses 
1 
2 
1 
5 
6 
2 
3 
Therefore, the mean number of plants per house is 8.1. We have used direct method as numerical values of C.I. and f_{i} are small.
2. Consider the following distribution of daily wages of 50 workers of a factory
Daily wages (in Rs.)  100120  120140  140160  160180  180200 
Number of workers  12  14  8  6  10 
3. 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 c)  1113  1315  1517  1719  1921  2123  2335 
Number of children  7  6  9  13  f  5  4 
4. 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  6568  6871  7174  7477  7780  8083  8386 
Number of women  2  4  3  8  7  4  2 
5. 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  5052  5355  5658  5961  6264 
Number of boxes  15  110  135  115  25 
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
6. The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.
Daily expenditure(in c)  100150  150200  200250  250300  300350 
Number of households  4  5  12  2  2 
7. To find out the concentration of SO_{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 SO_{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 
8. 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  06  610  1014  1420  2028  2838  3840 
Number of students  11  10  7  4  4  3  1 
9. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean
literacy rate.
Literacy rate (in %)  4555  5565  6575  7585  8598 
Number of cities  3  10  11  8  3 
Exercise 14.2
1. The following table shows the ages of the patients admitted in a hospital during a year:
Age (in years)  515  1525  2535  3545  4555  5565 
Number of patients  6  11  21  23  14  5 
2. The following data gives the information on the observed lifetimes (in hours) of 225
electrical components:
Lifetime (in hours)  020  2040  4060  6080  80100  100120 
Frequency  10  35  52  61  38  29 
3. 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  Number of families 
10001500  24 
15002000  40 
20002500  33 
25003000  28 
30003500  30 
35004000  22 
40004500  16 
45005000  7 
4. The following distribution gives the statewise teacherstudent ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures
No of Students per teacher  Number of states / U.T 
1520  3 
2025  8 
2530  9 
3035  10 
3540  3 
4045  0 
4550  0 
5055  2 
Most states/U.T. have 30.62 students per teacher and average number of students per teacher is 29.22.
5. The given distribution shows the number of runs scored by some top batsmen of the world in one day international cricket matches.
Run Scored  Number of Batsman 
30004000  4 
40005000  18 
50006000  9 
60007000  7 
70008000  6 
80009000  3 
900010000  1 
1000011000  1 
6. A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data:
Number of cars  Frequency 
010  7 
1020  14 
2030  13 
3040  12 
4050  20 
5060  11 
6070  15 
7080  8 
Exercise 14.3
1. The following frequency distribution gives the monthly consumption of an electricity of 68 consumers in a locality. Find the median, mean and mode of the data and compare them.
Monthly consumption(in units)  No. of customers 
6585  4 
85105  5 
105125  13 
125145  20 
145165  14 
165185  8 
185205  4 
2. If the median of a distribution given below is 28.5 then, find the value of x & y.
Class Interval  Frequency 
010  5 
1020  x 
2030  20 
3040  15 
4050  y 
5060  5 
Total  60 
3. The Life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to the persons whose age is 18 years onwards but less than the 60 years.
Age (in years)  Number of policy holder 
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 
4. The lengths of 40 leaves in a plant are measured correctly to the nearest millimeter, and the data obtained is represented as in the following table:
Length (in mm)  Number of leaves 
118126  3 
127135  5 
136144  9 
145153  12 
154162  5 
163171  4 
172180  2 
5. The following table gives the distribution of a life time of 400 neon lamps.
Lifetime (in hours)  Number of lamps 
15002000  14 
20002500  56 
25003000  60 
30003500  86 
35004000  74 
40004500  62 
45005000  48 
6. In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows:
Number of letters  14  47  710  1013  1316  1619 
Number of surnames  6  30  40  16  4  4 
7. The distributions of below give a weight of 30 students of a class. Find the median weight of a student.
Weight(in kg)  4045  4550  5055  5560  6065  6570  7075 
Number of students  2  3  8  6  6  3  2 
Exercise 14.4
1. The following distribution gives the daily income of 50 workers if a factory. Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.
Daily income in Rupees  100120  120140  140160  160180  180200 
Number of workers  12  14  8  6  10 
2.During the medical checkup of 35 students of a class, their weights were recorded as follows:
Weight in kg  Number of students 
Less than 38  0 
Less than 40  3 
Less than 42  5 
Less than 44  9 
Less than 46  14 
Less than 48  28 
Less than 50  32 
Less than 52  35 
Hence, median is 46.5 kg.
Table for median :
3. The following tables gives production yield per hectare of wheat of 100 farms of a village.
Production Yield  5055  5560  6065  6570  7075  7580 
Number of farms  2  8  12  24  38  16 