Statistics

CBSE Class 10 — Maths — Previous Year Questions

62 questions157 total marksVSA: 15MCQ: 17Case-Study: 8SA: 7LA: 15

Q1.VSA1 mark(2020)Easy

If the mean of first

n

natural numbers is

15

n

Q2.VSA1 mark(2020)Easy

Find the class-marks of the classes 10-25 and 35-55.

Q3.VSA1 mark(2020)Easy

Using the empirical formula, find the mode of a distribution whose mean is 8.32 and the median is 8.05.

Q4.VSA1 mark(2020)Easy

What is the arithmetic mean of first

n

natural numbers?

Q5.MCQ1 mark(2020)Easy

The mean and median of a distribution are 14 and 15 respectively. The value of mode is

Q6.MCQ1 mark(2020)Easy

\overset{x}{ˉ} = a + \frac{\sum f _{i} u _{i}}{\sum f _{i}} \times h

u_{i}

Q7.MCQ1 mark(2023)Medium

The distribution below gives the marks obtained by 80 students on a test:

| Marks | Less than

10

20

30

40

50

60

75

80

|
|-------|---------------|---------------|---------------|---------------|---------------|---------------|---------------|---------------|
| Number of Students |

3

12

27

57

75

80

| | |

The modal class of this distribution is:
(A)

10

20

20

30

30

40

50

60

Q8.MCQ1 mark(2023)Easy

If the value of each observation of a statistical data is increased by 3, then the mean of the data
(A) remains unchanged
(B) increases by 3
(C) increases by 6
(D) increases by

3 n

Q9.MCQ1 mark(2023)Easy

The empirical relation between the mode, median and mean of a distribution is:

Q10.MCQ1 mark(2023)Easy

If the mean and the median of a data are

12

15

respectively, then its mode is:

Q11.MCQ1 mark(2023)Easy

If every term of the statistical data consisting of

n

terms is decreased by

2

, then the mean of the data:

Q12.MCQ1 mark(2024)Medium

x_{1}, x_{2}, \dots, x_{n}

with respective frequencies

f_{1}, f_{2}, \dots, f_{n}

\sum f_{i} (x_{i} - \overset{x}{ˉ})

Q13.MCQ1 mark(2024)Easy

The middle most observation of every data arranged in order is called:

Q14.MCQ1 mark(2024)Easy

If value of each observation in a data is increased by

2

, then median of the new data

Q15.MCQ1 mark(2024)Easy

After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She requires to calculate ______ of marks.

Q16.MCQ1 mark(2024)Easy

If the difference of mode and median of a data is

24

, then the difference of its median and mean is:

Q17.MCQ1 mark(2024)Easy

2, 9, x + 6, 2 x + 3, 5, 10, 5

; if the mean is 7, then the value of

x

Q18.MCQ1 mark(2025)Easy

Mode and Mean of a data are

15 x

18 x

, respectively. Then the median of the data is:

Q19.MCQ1 mark(2025)Easy

2, 9, x + 6, 2 x + 3, 5, 10, 5

is 7, then the value of

x

Q20.MCQ1 mark(2025)Easy

The cumulative frequency for calculating median is obtained by adding the frequencies of all the:

Q21.MCQ1 mark(2025)Easy

If mean and median of given set of observations are 10 and 11 respectively, then the value of mode is:

Q22.VSA2 marks(2020)Medium

Find the mean of the following distribution:

| Class | 3-5 | 5-7 | 7-9 | 9-11 | 11-13 |
|---|---|---|---|---|---|
| Frequency | 5 | 10 | 10 | 7 | 8 |

Q23.VSA2 marks(2020)Medium

Find the mode of the following data:

| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | 120-140 |
|---|---|---|---|---|---|---|---|
| Frequency | 6 | 8 | 10 | 12 | 6 | 5 | 3 |

Q24.VSA2 marks(2020)Medium

Compute the mode for the following frequency distribution:

| Size of items (in cm) | 0-4 | 4-8 | 8-12 | 12-16 | 16-20 | 20-24 | 24-28 |
|---|---|---|---|---|---|---|---|
| Frequency | 5 | 7 | 9 | 17 | 12 | 10 | 6 |

Q25.VSA2 marks(2020)Medium

Find the value of

p

, if the mean of the following distribution is 7.5.

| Classes | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | 12-14 |
|---|---|---|---|---|---|---|
| Frequency (

f_{i}

) | 6 | 8 | 15 |

p

Q26.VSA2 marks(2020)Easy

Find the mode of the following distribution:

| Classes | 10-20 | 20-40 | 40-60 | 60-80 | 80-100 |
|---|---|---|---|---|---|
| Frequency | 10 | 8 | 12 | 16 | 4 |

Q27.VSA2 marks(2020)Medium

From the following distribution, find the median:

| Classes | 500-600 | 600-700 | 700-800 | 800-900 | 900-1000 |
|---|---|---|---|---|---|
| Frequency | 36 | 32 | 32 | 20 | 30 |

Q28.VSA2 marks(2020)Medium

Find the mode of the following distribution:

| Marks |

0

10

10

20

20

30

30

40

40

50

50

60

|
|-------|----------|-----------|-----------|-----------|-----------|----------|
| Number of Students |

4

6

7

12

5

6

Q29.VSA2 marks(2022)Easy

Find the mode of the following frequency distribution:

| Class |

10

20

20

30

30

40

40

50

50

60

|
|-------|-----------|-----------|-----------|-----------|----------|
| Frequency |

15

10

12

17

4

Q30.VSA2 marks(2022)Medium

If mode of the following frequency distribution is

55

, then find the value of

x

0

15

15

30

30

45

45

60

60

75

75

90

|
|-------|----------|-----------|-----------|-----------|-----------|----------|
| Frequency |

10

7

x

15

10

12

Q31.VSA2 marks(2022)Medium

The mode of a grouped frequency distribution is 75 and the modal class is

65

80

. The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8. Find the frequency of the modal class.

Q32.VSA2 marks(2022)Easy

Find the mean of the following frequency distribution:

| Class |

1

5

5

9

9

13

13

17

|
|-------|---------|---------|----------|-----------|
| Frequency |

4

8

7

6

Q33.Case-Study2 marks(2022)Medium

Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not only make our body healthy but also achieve inner peace and calmness. The International Yoga Day is celebrated on

2 1^{s t}

of June every year since 2015.

$Yoga meditation silhouette$

To promote Yoga, Green park society in Pune organised a 7-day Yoga camp in their society. The number of people of different age groups who enrolled for this camp is given as follows:

| Age Group |

15

25

25

35

35

45

45

55

55

65

65

75

75

85

|
|-----------|-----------|-----------|-----------|-----------|-----------|-----------|----------|
| Number of People |

8

10

15

25

40

24

18

|

Based on the above, find the following:
(a) Find the median age of people enrolled for the camp.

Q34.Case-Study2 marks(2022)Hard

x

more people of age group

63

75

had enrolled for the camp, the mean age would have been 58. Find the value of

x

Q35.Case-Study2 marks(2023)Medium

OR part of Q37(II): Find the mean rainfall in this season.

Q36.SA3 marks(2022)Medium

For what value of

x

, is the median of the following frequency distribution

34.5

0

10

10

20

20

30

30

40

40

50

50

60

60

70

|
|-------|----------|-----------|-----------|-----------|-----------|-----------|----------|
| Frequency |

3

5

11

10

x

3

2

Q37.SA3 marks(2022)Medium

Following is the daily expenditure on lunch by

30

employees of a company:

| Daily Expenditure (in Rupees) | Number of Employees |
|-------------------------------|--------------------|
|

100

120

8

120

140

3

140

160

8

160

180

6

180

200

5

|

Find the mean daily expenditure of the employees.

Q38.SA3 marks(2022)Medium

The mean of the following frequency distribution is

25

. Find the value of

f

0

10

10

20

20

30

30

40

40

50

|
|-------|----------|-----------|-----------|-----------|----------|
| Frequency |

5

18

15

f

6

Q39.SA3 marks(2022)Medium

Find the mean of the following data using assumed mean method:

| Class |

0

5

5

10

10

15

15

20

20

25

|
|-------|---------|----------|-----------|-----------|----------|
| Frequency |

8

7

10

13

12

Q40.SA3 marks(2022)Medium

50

students of class X of a school are recorded and following data is obtained:

| Height (in cm) |

130

135

135

140

140

145

145

150

150

155

155

160

|
|----------------|-------------|-------------|-------------|-------------|-------------|-------------|
| Number of Students |

4

11

12

7

10

6

|

Find the median height of the students.

Q41.SA3 marks(2023)Medium

Find the mean of the following frequency distribution:

| Classes |

25 - 30

30 - 35

35 - 40

40 - 45

45 - 50

50 - 55

55 - 60

|
|---------|-----------|-----------|-----------|-----------|-----------|-----------|----------|
| Frequency |

14

22

16

6

5

3

4

Q42.SA3 marks(2024)Easy

In a test, the marks obtained by

100

students (out of

50

) are given below:

| Marks obtained |

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

|
|----------------|----------|-----------|-----------|-----------|----------|
| Number of students |

12

23

34

25

6

|

Find the mean marks of the students.

Q43.LA4 marks(2020)Medium

The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village:

| Production yield/hect. | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 |
|---|---|---|---|---|---|---|
| No. of farms | 4 | 6 | 16 | 20 | 30 | 24 |

Change the distribution to a 'more than' type distribution and draw its ogive.

Q44.LA4 marks(2020)Hard

The median of the following data is

525

. Find the values of

x

y

, if total frequency is

100

.

| Class | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 | 500-600 | 600-700 | 700-800 | 800-900 | 900-1000 |
|---|---|---|---|---|---|---|---|---|---|---|
| Frequency | 2 | 5 |

x

| 12 | 17 | 20 |

y

Q45.LA4 marks(2020)Medium

The mean of the following frequency distribution is 18. The frequency

f

in the class interval

19 - 21

is missing. Determine

f

.

| Class interval | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |
|---|---|---|---|---|---|---|---|
| Frequency | 3 | 6 | 9 | 13 |

f

Q46.LA4 marks(2020)Medium

The following table gives the production yield per hectare of wheat of 100 farms of a village.

| Production yield | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 |
|---|---|---|---|---|---|---|
| No. of farms | 4 | 6 | 16 | 20 | 30 | 24 |

Change the distribution to a 'more than or equal to' type distribution and draw its ogive.

Q47.LA4 marks(2020)Medium

For the following frequency distribution, draw a cumulative frequency curve of 'more than' type and hence obtain the median value.

| Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
|---|---|---|---|---|---|---|---|
| Frequency | 5 | 15 | 20 | 23 | 17 | 11 | 9 |

Q48.LA4 marks(2020)Medium

Draw a 'more than' cumulative frequency curve for the following distribution. Also, find the median from the graph.

| Weight (in kg) | 40-44 | 44-48 | 48-52 | 52-56 | 56-60 | 60-64 | 64-68 |
|---|---|---|---|---|---|---|---|
| Number of Students | 7 | 12 | 33 | 47 | 20 | 11 | 5 |

Q49.LA4 marks(2020)Medium

For the following data, draw a 'less than' ogive and hence find the median of the distribution.

| Age (In years) |

0

10

10

20

20

30

30

40

40

50

50

60

60

70

|
|----------------|----------|-----------|-----------|-----------|-----------|-----------|----------|
| Number of persons |

5

15

20

25

15

11

9

Q50.LA4 marks(2020)Hard

The distribution given below shows that the number of wickets taken by bowler in one-day cricket matches. Find the mean and the median of the number of wickets taken.

| Number of wickets |

20

60

60

100

100

140

140

180

180

220

220

260

|
|-------------------|-----------|------------|-------------|-------------|-------------|------------|
| Number of bowlers |

7

5

16

12

2

3

Q51.Case-Study4 marks(2023)Medium

India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country.

$India Meteorological Department logo$

It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018:

| Rainfall (mm) | Number of Sub-divisions |
|---------------|------------------------|
|

200

400

2

400

600

4

600

800

7

800

1000

4

1000

1200

2

1200

1400

3

1400

1600

1

1600

1800

1

|

Based on the above information, answer the following questions:
(I) Write the modal class.
(II) Find the median of the given data.

OR

(II) Find the mean rainfall in this season.
(III) If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-divisions had good rainfall?

Q52.Case-Study4 marks(2024)Medium

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game.

$BINGO$

The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.

| Numbers announced |

0 - 15

15 - 30

30 - 45

45 - 60

60 - 75

|
|---|---|---|---|---|---|
| Number of times (

f_{i}

8

9

10

12

9

|

Based on the above information, answer the following:
(i) Write the median class.
(ii) When first ball was picked up, what was the probability of picking up an even number?
(iii) (a) Find median of the given data.

OR

(b) Find mode of the given data.

Q53.Case-Study4 marks(2024)Medium

Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows:

$Students at starting blocks of a running race$

| Time (in seconds) |

0 - 20

20 - 40

40 - 60

60 - 80

80 - 100

|
|---|---|---|---|---|---|
| Number of students |

8

10

13

6

3

|

Based on the above, answer the following questions:
(i) What is the median class of the above given data?
(ii) (a) Find the mean time taken by the students to finish the race.
OR
(ii) (b) Find the mode of the above given data.
(iii) How many students took time less than 60 seconds?

Q54.Case-Study4 marks(2024)Medium

Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows:

$Students at starting blocks of a running race$

| Time (in seconds) |

0 - 20

20 - 40

40 - 60

60 - 80

80 - 100

|
|---|---|---|---|---|---|
| Number of students |

8

10

13

6

3

|

Based on the above, answer the following questions:
(i) What is the median class of the above given data?
(ii) (b) Find the mode of the above given data.
(iii) How many students took time less than 60 seconds?

Q55.Case-Study4 marks(2025)Medium

Case Study 3:

The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results.

$IMD Logo$

The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.

| Rainfall (mm) | No. of Sub-divisions |
|---------------|---------------------|
|

200 - 400

3

400 - 600

4

600 - 800

7

800 - 1000

4

1000 - 1200

3

1200 - 1400

3

|

Based on the information given above, answer the following questions:
(i) Write the modal class.
(ii) (a) Find the median of the given data.
**OR**
(b) Find the mean rainfall in the season.
(iii) If a sub-division having at least 800 mm rainfall during monsoon season is considered a good rainfall sub-division, then how many sub-divisions had good rainfall?

Q56.LA5 marks(2023)Medium

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 mean and median of the following data.

| Number of cars |

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

70 - 80

|
|---|---|---|---|---|---|---|---|---|
| Frequency (periods) |

7

14

13

12

20

11

15

8

Q57.LA5 marks(2023)Hard

The monthly expenditure on milk in 200 families of a Housing Society is given below:

| Monthly Expenditure (in ₹) | 1000-1500 | 1500-2000 | 2000-2500 | 2500-3000 | 3000-3500 | 3500-4000 | 4000-4500 | 4500-5000 |
|---|---|---|---|---|---|---|---|---|
| Number of families | 24 | 40 | 33 |

x

| 30 | 22 | 16 | 7 |

Find the value of

x

and also, find the median and mean expenditure on milk.

Q58.LA5 marks(2023)Medium

250

apples of a box were weighed and the distribution of masses of the apples is given in the following table:

| Mass (in grams) |

80 - 100

100 - 120

120 - 140

140 - 160

160 - 180

|
|---|---|---|---|---|---|
| Number of apples |

20

60

70

x

60

|

(i) Find the value of

x

and the mean mass of the apples.
(ii) Find the modal mass of the apples.

Q59.LA5 marks(2024)Medium

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

| Age (in years) |

5 - 15

15 - 25

25 - 35

35 - 45

45 - 55

55 - 65

|
|----------------|----------|-----------|-----------|-----------|-----------|----------|
| Number of patients |

6

11

21

23

14

5

|

Find the mode and mean of the data given above.

Q60.LA5 marks(2025)Hard

Find the missing frequency '

f

' in the following table, if the mean of the given data is 18. Hence find the mode.

| Daily Allowance | Number of Children |
|-----------------|--------------------|
|

11 - 13

7

13 - 15

6

15 - 17

9

17 - 19

13

19 - 21

f

21 - 23

5

23 - 25

4

Q61.LA5 marks(2025)Medium

Find the Mean and Mode of the following frequency distribution:

| Class | Frequency |
|-------|-----------|
|

0 - 10

8

10 - 20

7

20 - 30

15

30 - 40

20

40 - 50

12

50 - 60

8

60 - 70

10

Q62.LA5 marks(2025)Medium

The following table shows the number of patients of different age group who were discharged from the hospital in a particular month:

| Age (in years) | Number of Patients Discharged |
|----------------|-------------------------------|
|

5 - 15

6

15 - 25

11

25 - 35

21

35 - 45

23

45 - 55

14

55 - 65

5

|
| **Total** | **80** |

Find the 'mean' and the 'mode' of the above data.

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