Statistics Class 10
Master Statistics Class 10 with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
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NCERT Solutions
Statistics Class 10 – NCERT Solutions
Each question below opens its complete step-by-step Teachoo solution.
Ex 13.1
9 questionsEx 13.1, 1
Ex 13.1,1 teachoo.com
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 housesin a
locality. Find the mean number of plants per house. Which method
did you use & why?
0-2 1
2-4 2
4-6 1
6-8 5
8-10 6
10-12 2
12-14 3
Ex 13.1, 2
Ex 13.1, 2 teachoo.com
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 an appropriate method.
500 - 520 12
520 - 540 14
540 - 560 8
560 - 580 6
580 - 500 10
Ex 13.1, 3
Ex 13.1, 3 teachoo.com
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.
allowance workers
(in Rs} (fi)
11-13 7
13-15 6
15-17 9
17-19 13
19-21 f
21-23 5
23-25 4
Ex 13.1, 4
Ex13.1, 4 teachoo.com
Thirty women were examined in a hospital by a doctor and the
number of heart beats per minute were recorded and
summarized as follows. Fine the mean heart beats per minute
for these women, choosing a suitable method.
beats per minute women
65 — 68 2
68-71 4
71-74 3
74-77 8
77-80 7
80 — 83 4
83 - 86 2
Ex 13.1, 5
Ex 13.1,5 teachoo.com
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. Find the mean number of mangoes kept in a
packing box. Which method of finding the mean did you choose?
50-52 15
53-55 110
56-58 135
59-61 115
62 — 64 25
Ex 13.1, 6
Ex 13.1, 6 teachoo.com
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
Peritry 100-150 150-200 200-250 250-300 300-350
(in Rs)
Number of 4 5 2 2 2
households
Ex 13.1, 7
Ex 13.1, 7 teachoo.com
To find out the concentration of SO, 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. Find the mean concentration of SO, in the air.
Concentration of
lin pom) 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
Ex 13.1, 8
Ex 13.1, 8 (Method 1 — Direct Method) teachoo.com
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.
0-6 11
6-10 10
10-14 7
14-20 4
20 - 28 4
28 - 38 3
38-40 1
Here Class Size is not same,
So, we solve by Direct Method
Ex 13.1, 9
teachoo.com
Ex 13.1, 9
The following table gives the literacy rate (in percentage) of 35
cities. Find the mean literacy rate.
Literacy rate
45-55 55-65 65-75 75-85 85-95
{in %)
Number of
3 10 11 8 3
cities
Ex 13.2
6 questionsEx 13.2, 1
Ex 13.2,1 teachoo.com
The following table shows the ages of the patients admitted in a
hospital during a year: Find the mode and the mean of the data given
above. Compare and interpret the two measures of central tendency.
_ Age 5-15 15-25 25-35 35-45 45-55 55-65
(in years)
Number of Hig 11 21 23 14 5
patients
Finding Mean first
Ex 13.2, 2
Ex 13.2, 2 teachoo.com
The following data gives the information on the observed lifetimes
(in hours) of 225 electrical components. Determine the modal
lifetimes of the components.
Lifetimes
0-20 20-40 40-60 60-80 80-100 100-120
(in hours)
Frequency 10 35 52 61 38 29
Ex 13.2, 3
Ex 13.2, 3 teachoo.com
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.
(in Rs.) 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
Ex 13.2, 4
Ex 13.2, 4 teachoo.com
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 Number of
students / teacher| 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
Ex 13.2, 5
Ex 13.2, 5 teachoo.com
The given distribution shows the number of runs scored by some
top batsmen of the world in one-day internatid No. of
: Runs scored | batsmen
Find mode of the data (fa
t.
3000 — 4000 4 fo
Mode =/+ fifo _ xh
2f, fo hf,
Modal class = Interval with highest frequency 5000 —- 6000 9 f,
= 4000 — 5000 6000 — 7000 7
7000 — 8000 6
where /= lower limit of modal class = 4000
h=class-interval = 4000-3000 = 1000 8000-90003
9000 — 10000 1
f, = frequency of the modal class = 18
10000-11000 1
fg= frequency of class before modal class =4
f, = frequency of class after modal class = 9
Ex 13.2, 6
Ex 13.2, 6 teachoo.com
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: MDD RM TL Ua g
cars (fa
hi-f 0-10 7
Mode = /+—+—*— xh
2f, fo fe 10-20 14
Modal class = Interval with highest frequency 20-30 13
= 40-50 30-40 12 fy
where /= lower limit of modal class = 40 PF
h=class-interval = 10-0 =10 50-60 11 f,
f, = frequency of the modal class = 20 60-70 15
fg= frequency of class before modal class = 12
f, = frequency of class after modal class = 11
Ex 13.3
7 questionsEx 13.3, 1
€x 13.3, 1 teachoo.com
The following frequency distribution gives the monthly consumption
of electricity of 68 consumers of a locality. Find the median, mean
and mode of the data and compare them.
65-85 4
85 - 105 5
105-125 13
125-145 20
145-165 14
165 - 185 8
185 — 205 4
Ex 13.3, 2
teachoo.com
Ex 13.3, 2
If the median of the distribution given below is 28.5, find the values
of x and y.
Class Frequency
interval (fi)
0-10 5
10-20 x
20-30 20
30-40 1s
40-50 y
50-60 5
Total 60
Ex 13.3, 3
Ex 13.3, 3 teachoo.com
A life insurance agent found the following data for distribution of
ages of 100 policy holders. Calculate the median age, if policies
are given only to persons having age 18 years onwards but less
than 60 year.
(in years) | 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
Ex 13.3, 4
Ex 13.3, 4 teachoo.com
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. Find the median length of the leaves
(in mm) leaves (f;)
118 - 126 3
127 - 135 5
136 - 144 9
145 - 153 12
154 - 162 5
163 - 171 4
172 - 180 2
Ex 13.3, 5
Ex 13.3,5 teachoo.com
Find the following table gives the distribution of the life time of 400
neon lamps:
Life time Number of
(in hours) lamps
1500 - 2000 14
2000 - 2500 56
2500 - 3000 60
3000 - 3500 86
3500 - 4000 74
4000 - 4500 62
4500 - 5000 48
Find the median life time of a lamp.
Ex 13.3, 6
Ex 13.3, 6 teachoo.com
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.
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
Number of
1-4 4-7 7-10 10-13 13-16 16-19
letters
Number of
6 30 40 16 4 4
surnames
Ex 13.3, 7
Ex 13.3, 7 teachoo.com
The distribution below gives the weights of 30 students of a class.
Find the median weight of the students.
WOrm(heam 40-45 45-50 50-55 55-60 60-65 65-70 70-75
Number of
2 4 8 6 6 3 2
students
Examples
9 questionsExample 1
teachoo.co
Example 1 m
The marks obtained by 30 students of Class X of a certain school in
a Mathematics paper consisting of 100 marks are presented in
table below. Find the mean of the marks obtained by the students.
Marks
10 20 36 40 50 56 60 70 72 80 88 92 95
obtained
Number of
113 4 3 2 44 1 1 2 3 «21
student
Example 2
Example 2 teachoo.com
The table below gives the percentage distribution of female
teachers in the primary schools of rural areas of various states and
union territories (U.T.) of India. Find the mean percentage of female
teachers by all the three methods discussed in this section.
Percentage of Number of
female teachers States/U.T.
15-25 6
25-35 11
35-45 7
45-55 4
55-65 4
65-75 2
75-85 1
Example 3
Example 3 (Method 1 — Direct Method) teachoo.com
The distribution below shows the number of wickets taken by
bowlers in one-day cricket matches. Find the mean number of
wickets by choosing a suitable method. What does the mean signify?
Here Class Size is not Number | Number of | Class mark
same, of wickets | bowler (f;} (x;)}
So, we solve by Direct 20-60 7 40 7x 40= 280
Method 60-100 5 80 5 x 80= 400
100-150 16 125 16x125=2000
Mean(x) = oie 150-250 12 200 12x 200=2400
- 300 2x 300=600
- 68R0 250-350 2 x
45 350-450 3 400 3x 400=1200
X = 152.89
yf =45 df x; = 6880
Thus, Mean signifies that on average, 45 bowlers take 152.89 wickets
Example 4
Example 4 teachoo.com
The wickets taken by a bowler in 10 cricket matches are as
follows:
2 6 4 5 02 1 3 2 3
Find the mode of the data.
Mode is the observation which repeats the most times.
Here 2 occurs three times
So, Mode = 2
Example 5
Example 5 teachoo.com
A survey conducted on 20 households in a locality by a group of
students resulted in the following frequency table for the number
of family members in a household. Find the mode of this data.
Family | Number of
Mode =/+ fivfo oh size | families (f;)
2f, fo hf,
1-3 7 fy
Modal class = Interval with highest frequency
5-7 2 f,
=3-5
7-9 2
where /= lower limit of modal class = 3
9-11 1
h=class-interval = 3-1=2
f, = frequency of the modal class = 8
fy = frequency of the class before modal class = 7
f, = frequency of the class after modal class = 2
Example 6
Example 6 teachoo.com
The marks distribution of 30 students in a mathematics examination
are given in Table 14.3 of Example 1. Find the mode of this data. Also
compare and interpret the mode and the mean.
- Class No. of
Mode =/ + _Sifo_, h
2f1 fo fa interval | students (f,)
Modal class = Interval with highest frequency 10-25 2
= 40-55 25-40 3 fy
where / = lower limit of modal class = 40
55-70 6 f,
h=class-interval =25—10=15
70-85 6
f, = frequency of the modal class =7
85-100 6
fg = frequency of class before modal class = 3
f, = frequency of class after modal class = 6
Example 7
Example 7 teachoo.com
A survey regarding the heights (in cm) of 51 girls of Class X of a
school was conducted and the following data was obtained
Find the median height.
Height Number of
(in cm) girls
Less than 140 4
Less than 145 11
Less than 150 29
Less than 155 40
Less than 160 46
Less than 165 51
Example 8
Example 8 teachoo.com
The median of the following data is 525. Find the values of x and y,
if the total frequency is 100.
i
0-100 2
100 — 200 5
200 — 300 x
300 — 400 12
400 — 500 17
500 — 600 20
600 — 700 y
700 — 800 9
800 — 900 7
900 — 1000 4
Question 1
Example 9 teachoo.com
The annual profits earned by 30 shops of a shopping complexina
locality give rise to the following distribution :
(in lakh Rs) shops
More than or equal to 5 30
More than or equal to 10 28
More than or equal to 15 16
More than or equal to 20 14
More than or equal to 25 10
More than or equal to 30 7
More than or equal to 35 3
Draw both ogives for the data above. Hence obtain the median
profit.
Case Based Questions (MCQ)
4 questionsQuestion 1
The COVID-19 pandemic, also known as coronavirus pandemic, is an ongoing pandemic of coronavirus disease caused by the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) among humans. The following tables shows the age distribution of case admitted during a day in two different hospitals
Refer to Table 1
Question 1
The average age for which maximum cases occurred is
(a) 32.24
(b) 34.36
(c) 36.82
(d) 42.24
Question 2
The upper limit of modal class is
(a) 15
(b) 25
(c) 35
(d) 45
Question 3
The mean of the given data is
(a) 26.2
(b) 32.4
(c) 33.5
(d) 35.4
Refer to table 2
Question 4
The mode of the given data is
(a) 41.4
(b) 48.2
(c) 55.3
(d) 64.6
Question 5
The median of the given data is
(a) 32.7
(b) 40.2
(c) 42.3
(d) 48.6
Question 2
Electricity energy consumption is the form of energy consumption that uses electric energy. Global electricity consumption continues to increase faster than world population, leading to an increase in the average amount of electricity consumed per person (per capita electricity consumption).
A survey is conducted for 56 families of a Colony A. The following tables gives the weekly consumption of electricity of these families.
Weekly consumption (in units)
0-10
10-20
20-30
30-40
40-50
50-60
No. of families
16
12
18
6
4
0
Refer to data received from Colony A
Question 1
The median weekly consumption is
(a) 12 units
(b) 16 units
(c) 20 units
(d) None of these
Refer to data received from Colony A
Question 2
The mean weekly consumption is
(a) 19.64 units
(b) 22.5 units
(c) 26 units
(d) None of these
Refer to data received from Colony A
Question 3
The modal class of the above data is
(a) 0 – 10
(b) 10 – 20
(c) 20 – 30
(d) 30 – 40
Refer to data received from Colony B
Question 4
The modal weekly consumption is
(a) 38.2 units
(b) 43.6 units
(c) 26 units
(d) 32 units
Refer to data received from Colony B
Question 5
The mean weekly consumption is
(a) 15.65 units
(b) 32.8 units
(c) 38.75 units
(d) 48 units
Question 3
Question The weights (in kg) of 50 wrestlers are recorded in the following table: Question 1 What is the upper limit of modal class. (a) 120 (b) 130 (c) 100 (d) 150 Modal class is class with highest frequency
View solutionQuestion 4
Question The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching center are given as follows. Question 1 What is the modal class of the given data? (a) 85-100 (b) 100-115 (c) 115-130 (d) 130-145 Modal class is class with highest frequency
View solutionLess than, and more than Ogive
3 questionsQuestion 1
Ex 14.4, 1 teachoo.com
The following distribution gives the daily income of 50 workers of a
factory.
Daily income
100-120 120-140 140-160 160-180 180-200
(in 3)
Number of
12 14 8 6 10
workers
Convert the distribution above to a less than type cumulative
frequency distribution, and draw its ogive.
Question 2
Ex 14.4, 2 teachoo.com
During the medical check-up of 35 students of a class, their weights
were recorded as follows:
(in kg) 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
Draw a less than type ogive for the given data. Hence obtain the
median weight from the graph verify the result by using the formula.
Question 3
Ex 14.4, 3 teachoo.com
The following table gives production yield per hectare of wheat of
100 farms of a village.
Production
50-55 55-60 60-65 65-70 70-75 75-80
yield (in kg/ha)
Number of
2 8 12 24 38 16
farms
Change the distribution to a more than type distribution and draw
ogive.
Why Learn This With Teachoo?
Statistics is Chapter 14 of NCERT Class 10 Mathematics. It covers mean, median and mode for grouped data and cumulative-frequency graphs called ogives. Students use direct, assumed-mean and step-deviation methods, identify median and modal classes and interpret less-than and more-than cumulative frequencies. Teachoo provides Exercises 13.1 to 13.3, examples and case-based questions.
Mean of grouped data
For class intervals, each class is represented by its midpoint xᵢ. The direct mean is Σfᵢxᵢ/Σfᵢ. Assumed-mean and step-deviation methods simplify arithmetic without changing the result. Students should choose a convenient assumed mean and equal class width where the step-deviation formula requires it.
Median and mode
To find the median, create cumulative frequencies and locate the class containing N/2. The grouped median formula uses the lower class boundary, cumulative frequency before the median class, median-class frequency and class width.
The modal class has the highest frequency. The grouped mode formula uses its frequency and those of adjacent classes. Class boundaries must be continuous before formulas are applied.
Ogives
A less-than ogive plots upper class boundaries against less-than cumulative frequency. A more-than ogive plots lower boundaries against more-than cumulative frequency. Their intersection estimates the median graphically. Axes, scale and cumulative direction must be labelled correctly.
Topics available on Teachoo
-
Exercises 13.1 to 13.3 and examples;
-
mean by direct, assumed-mean and step-deviation methods;
-
grouped mode;
-
grouped median;
-
less-than and more-than cumulative frequency;
-
less-than and more-than ogives;
-
case-based questions.
Learning outcomes
Students should be able to organise grouped data, select an efficient mean method and calculate mean, median and mode. They should construct cumulative-frequency tables, draw both ogives and estimate the median graphically.
Why is this chapter important?
Statistics turns data into interpretable summaries. It appears in economics, science, surveys and public information. Board questions test both calculation and the ability to identify correct classes, boundaries and frequencies.
How Teachoo helps
Teachoo separates every measure and graph type. Prepare a full table with class marks, frequencies and cumulative values before using formulas. Circle N/2 for median and the largest frequency for mode. For ogives, plot boundaries rather than class midpoints.
Important concept connections
Grouped statistics approximates many individual observations through intervals and representative class marks. Mean uses weighted arithmetic, median uses ordered cumulative position and mode uses the most concentrated class. Ogives connect data tables with coordinate graphs. Probability then uses frequency ideas to describe chance, so interpreting totals, relative frequency and cumulative counts accurately supports both chapters.
Board-exam and competency preparation
Statistics questions are long but highly structured. Build the table first and keep column headings visible: class mark, frequency, deviations, products or cumulative frequency. Check Σf against the total before using any formula. Select direct, assumed-mean or step-deviation method based on arithmetic convenience, not because one is more mathematically correct.
For median and mode, identify the relevant class before substitution and distinguish its ordinary frequency from cumulative frequency. In ogive questions, use class boundaries and consistent scales; a neat graph is part of the answer. Case-based tables may include a missing frequency. Translate the supplied mean, median or total into an equation and solve before completing the statistic.
Quick revision checklist
Find mean by all three methods, calculate grouped median and mode, solve one missing-frequency question and draw less-than and more-than ogives on the same axes. Verify total frequency at every stage.
Common mistakes to avoid
Do not divide by the number of classes instead of total frequency. Median class is determined through cumulative frequency; modal class through highest ordinary frequency. Convert inclusive intervals to continuous boundaries where necessary. Less-than and more-than ogives use different cumulative tables.
Deeper reasoning and concept connections
The strongest way to learn Statistics is to separate three layers: the object being studied, the rule that describes it and the reason the rule works. A correct numerical result is useful, but a complete mathematical answer also explains the relationship used. Students should compare examples and non-examples, change one condition at a time and observe whether the conclusion still holds.
This chapter is part of a longer progression. Its vocabulary and representations will appear again in algebra, geometry, data, measurement or higher problem-solving. Build links deliberately: translate pictures into statements, statements into operations and operations back into a sensible interpretation. If the final result cannot be explained in ordinary language, the method has probably been followed mechanically rather than understood.
How to solve unfamiliar and competency-based questions
When a question looks new, do not search memory for an identical example. Classify it. Decide whether it asks for recognition, calculation, representation, comparison, explanation or proof. Write the relevant definition or property first. Next, organise the data and select the shortest valid method. This converts an unfamiliar surface story into a familiar mathematical structure.
Use estimation and special cases as quality checks. Test zero, one, equal values, endpoints or a simple symmetric figure whenever they are permitted. A result that violates the diagram, scale, sign, unit or expected range is a signal to recheck the setup. In multi-part cases, carry forward only verified results so one early error does not silently contaminate every later answer.
What complete mastery looks like
For Statistics, a student should be able to define the central ideas in simple language, recognise them in different representations, solve routine questions accurately and explain the method used. They should also be able to correct a flawed solution, create an example satisfying given conditions and combine two ideas from the chapter in one problem. A reliable mastery test is to solve one direct question, one application question and one reasoning question without looking at notes, then explain all three aloud or in writing.
Keep a compact error log with four labels: concept, interpretation, calculation and presentation. Reattempt each error after a gap instead of rereading the answer immediately. Improvement comes from correcting the decision that caused the mistake, not from repeating questions whose method is already known.
Additional frequently asked questions
What should a student know before starting Statistics?
Revise the definitions, number operations, diagrams or notation used at the beginning of the chapter. The prerequisite list should be short: if an earlier skill blocks progress, repair that skill with two or three focused questions and return to the chapter.
How can a student check an answer in Statistics?
Use an independent check whenever possible: substitute the result, reverse the operation, estimate its size, compare it with the figure, test a simpler case or solve using another representation. A check should examine the mathematical condition, not merely repeat the same arithmetic.
How many questions are enough for strong preparation?
There is no fixed number. Stop counting questions and track coverage: every concept, every standard method, at least one mixed problem, one competency-based problem and every previously incorrect type should be solved independently. Ten varied, analysed questions are more valuable than fifty copied solutions.
How should Teachoo solutions be used without becoming dependent on them?
Attempt the question first and mark the exact step where progress stops. Read only enough of the solution to repair that step, close it and restart the question. Finally, solve a similar problem without help. This turns a solution into feedback rather than a substitute for thinking.
Frequently asked questions
Which mean method is best?
All give the same answer; choose the method that makes arithmetic simplest.
How is the median class found?
Locate the first cumulative frequency greater than or equal to N/2.
What does the intersection of two ogives represent?
Its x-coordinate provides a graphical estimate of the median.
Build the table correctly before touching the formula. Statistics errors almost always begin in the data organisation.