Chapter 13: Statistics

CBSE Class 10 Mathematics — Previous Year Questions 2026

Basic + Standard Mathematics | Chapterwise PYQ Collection

BASIC 2026

I. Multiple Choice Questions 1 Mark

BASIC

1. Class Marks & Median Class

The class mark of the median class of the following data is:

Class Interval 10 – 25 25 – 40 40 – 55 55 – 70 70 – 85 85 – 100
Frequency 2 3 7 6 6 6
(A) 40    (B) 55    (C) 47.5    (D) 62.5
Sets: 430/1/1, 430/1/2, 430/1/3
BASIC

2. Modal Class Limits

The lower limit of the modal class of the following distribution is:

Runs Scored 3000 – 4000 4000 – 5000 5000 – 6000 6000 – 7000
Number of Batsmen 5 10 9 8
(A) 3000    (B) 4000    (C) 5000    (D) 6000
Sets: 430/1/1, 430/1/2, 430/1/3
BASIC

The lower limit of the modal class for the following distribution is:

Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Number of Students 5 3 4 8 3
(A) 10    (B) 20    (C) 30    (D) 40
Sets: 430/3/1, 430/3/2, 430/3/3
BASIC

4. Mode Formula Definitions

In the formula of mode given by \[ \text{Mode} = l+ \left( \frac{f_1-f_0} {2f_1-f_0-f_2} \right)\times h, \] \(f_1\) denotes the:

(A) frequency of the modal class
(B) frequency of class preceding modal class
(C) frequency of class succeeding modal class
(D) cumulative frequency of modal class
Sets: 430/2/1, 430/2/2, 430/2/3
BASIC

5. Empirical Relationship

For a distribution, if \(\text{mean}=\text{median}=a\), then its mode is:

(A) \(3a\)    (B) \(2a\)    (C) \(a\)    (D) \(0\)
Sets: 430/2/1, 430/2/2, 430/2/3
BASIC

For a distribution, if mean = 15 and mode = 12, then its median is:

(A) 12    (B) 13    (C) 14    (D) 15
Sets: 430/3/1, 430/3/2, 430/3/3

II. Long Answer Questions 5 Marks

BASIC

7. Mean Calculation

Find the mean lifetime (in hours) of the electrical components:

Lifetime (in hours) Number of electrical components
0 – 2010
20 – 4035
40 – 6050
60 – 8060
80 – 10030
100 – 12015
Set: 430/1/1
BASIC

8. Median Calculation

Find the median age of the policy holders:

Age (in years) Number of policy holders
15 – 202
20 – 254
25 – 3018
30 – 3521
35 – 4033
40 – 4511
45 – 503
50 – 556
55 – 602
Set: 430/1/3
BASIC

Find the median length (in mm) of the leaves:

Length in (mm) Number of leaves
100 – 1208
120 – 1409
140 – 16012
160 – 1805
180 – 2006
Sets: 430/2/1, 430/2/2, 430/2/3
BASIC

10. Missing Frequencies

If the mean number of days a student was absent is 12, find the values of \(x\) and \(y\):

Number of days 0 – 4 4 – 8 8 – 12 12 – 16 16 – 20 20 – 24
Number of Absent students 1 8 \(x\) 6 5 \(y\)
Sets: 430/2/1, 430/2/2, 430/2/3
BASIC

The mean pocket allowance is ₹180. Find the value of \(f\). Hence find the mode of given data:

Weekly Pocket Allowance (in ₹) Number of Children
110 – 1307
130 – 1506
150 – 1709
170 – 19013
190 – 210\(f\)
210 – 2305
230 – 2504
Set: 430/3/2
BASIC

Find the value of \(x\). Hence find the mean daily expenditure:

Daily Expenditure (in ₹) Number of Households
500 – 7504
750 – 1000\(2x+1\)
1000 – 125012
1250 – 1500\(x\)
1500 – 17502
Set: 430/3/3
STANDARD 2026

I. Multiple Choice Questions 1 Mark

STANDARD

1. Empirical Relationship — Find Mode

Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is:

(A) 34    (B) 43    (C) 38.5    (D) 41.5
Set 30/4/1 Q18, Set 30/4/2 Q13
STANDARD

The mean and median of a data are 43 and 43.4 respectively. The mode of the distribution is:

(A) 43.4    (B) 42.4    (C) 44.2    (D) 49.3
Set 30/2/1 Q17
STANDARD

If the mean and mode of a data are 12 and 21 respectively, then its median is:

(A) 6    (B) 13.5    (C) 15    (D) 14
Set 30/1/2 Q18, Set 30/1/3 Q15
STANDARD

4. Step Deviation

While calculating mean, step deviation method was used \[ u=\frac{x-a}{h}. \] If \(\bar{x}=64,\ h=5\) and \(a=62.5\), then the value of \(\bar{u}\) is:

(A) 0.5    (B) 1.5    (C) 0.3    (D) 7.5
Set 30/5/1 Q6, Set 30/5/2 Q14, Set 30/5/3 Q11

II. Long Answer Type 5 Marks

STANDARD

5. Find Mean and Mode

Find the mean and mode of the following distribution:

Class Interval 400–450 450–500 500–550 550–600 600–650 650–700
Frequency 15 18 20 23 22 12
Set 30/5/2 Q35a
STANDARD

Find the mean and mode of the following distribution:

Class 0–15 15–30 30–45 45–60 60–75 75–90 90–105
Frequency 4 8 11 14 10 7 6
Set 30/3/1 Q32b, Set 30/4/1 Q35b
STANDARD

Find the median and mode of the following distribution:

Class Interval 0–15 15–30 30–45 45–60 60–75 75–90 90–105
Frequency 15 10 12 9 8 10 6
Set 30/5/1 Q34b

Type B: Finding Missing Frequencies

STANDARD

The median is 50 and the sum of all frequencies is 90. Find the values of \(p\) and \(q\).

Class 20–30 30–40 40–50 50–60 60–70 70–80 80–90
Frequency \(p\) 15 25 20 \(q\) 8 10
Set 30/4/1 Q35a
STANDARD

If the median is 32.5 and total frequency is 40, find \(x\) and \(y\).

Class 0–10 10–20 20–30 30–40 40–50 50–60 60–70
Frequency \(x\) 5 9 12 \(y\) 3 2
Set 30/4/2 Q33b, Set 30/5/2 Q35b
STANDARD

The mean is 28 and sum of frequencies is 100. Find \(p\) and \(q\).

Class Interval 0–10 10–20 20–30 30–40 40–50 50–60
Frequency 12 \(p\) 27 20 \(q\) 6
Set 30/5/1 Q34a
STANDARD

Mean is 53. Find the missing frequency \(p\), then find the mode.

Class Interval 0–20 20–40 40–60 60–80 80–100
Frequency 12 15 \(p\) 28 13
Set 30/5/3 Q33a

Type C: Special Data Formats

STANDARD

Compute the median of the following data:

Mid-value 115 125 135 145 155 165 175
Frequency 12 15 20 16 10 16 11
Set 30/5/3 Q33b
STANDARD

Find the median and the mode for the following distribution:

Score Number of students
0 and more80
10 and more77
20 and more72
30 and more65
40 and more55
50 and more43
60 and more28
70 and more16
80 and more10
90 and more8
100 and more0
Set 30/1/3 Q33
Chapter 13 — Statistics | CBSE Class 10 Mathematics PYQs 2026
Basic + Standard Mathematics