THE GOAL • CBSE CLASS 10

STATISTICS

Chapter 13 • Basic Mathematics • 2025 PYQs

CBSE 2025 Basic Mathematics Previous Year Questions Chapter-wise Collection

Chapter 13: Statistics

Unique Previous Year Questions extracted from the CBSE Class 10 Basic Mathematics 2025 question paper sets. Repetitive questions have been removed while retaining the major question types and variations.

I

Multiple Choice Questions

1. Class Mark Analysis
1 Mark
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
Set 430/1/1
2. Modal Class Identification
1 Mark
The following distribution shows the number of runs scored by some batsmen in test matches. The lower limit of the modal class 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
Set 430/1/1
3. Formula Component
1 Mark
In the formula \[ Mode=l+ \left( \frac{f_1-f_0} {2f_1-f_0-f_2} \right)\times h, \] the symbol \(f_1\) 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
Set 430/2/1
4. Empirical Relation – Literal
1 Mark
For a distribution, if \[ mean=median=a, \] then its mode is:
(A) \(3a\)
(B) \(2a\)
(C) \(a\)
(D) \(0\)
Set 430/2/1
5. Empirical Relation – Numerical
1 Mark
For a distribution, if \(mean=15\) and \(mode=12\), then its median is:
(A) 12
(B) 13
(C) 14
(D) 15
Set 430/3/1
6. Conceptual Property
1 Mark
Which of the following depends on all observations of a given data?
(A) Median
(B) Mean
(C) Range
(D) Mode
Set 430/5/1
7. Assumed Mean Method
1 Mark
To calculate the mean of a grouped data, Rahul used assumed mean method. He used \[ d=(x-A), \] where \(A\) is assumed mean. Then \(\bar{x}\) is equal to:
(A) \(A+\bar d\)
(B) \(A+h\bar d\)
(C) \(h(A+\bar d)\)
(D) \(A-h\bar d\)
Set 430/6/1
II

Long Answer Type Questions

8. Mean Lifetime Calculation
5 Marks
Find the mean lifetime (in hours) of the 200 electrical components from the data below:
Lifetime (in hours) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120
No. of Components 10 35 50 60 30 15
Set 430/1/1
9. Mean Consumption
5 Marks
The following frequency distribution gives the monthly consumption of electricity of 68 consumers. Find the monthly mean consumption:
Monthly Consumption (units) 50 – 100 100 – 150 150 – 200 200 – 250 250 – 300 300 – 350 350 – 400
Number of Consumers 4 5 13 20 14 8 4
Set 430/1/2
10. Median Age
5 Marks
Find the median age of the policyholders from the table below:
Age (in years) 15–20 20–25 25–30 30–35 35–40 40–45 45–50 50–55 55–60
No. of Holders 2 4 18 21 33 11 3 6 2
Set 430/1/3
11. Median Length – Leaves
5 Marks
Find the median length (in mm) of the 40 leaves represented below:
Length (in mm) 100 – 120 120 – 140 140 – 160 160 – 180 180 – 200
Number of Leaves 8 9 12 5 6
Set 430/2/1
12. Double Missing Frequency \((x,y)\)
5 Marks
If the mean number of days a student was absent is 12, find the values of \(x\) and \(y\) for a class of 30 students:
Number of days 0 – 4 4 – 8 8 – 12 12 – 16 16 – 20 20 – 24
Number of Absent students 1 8 \(x\) 6 5 \(y\)
Set 430/2/1
13. Median Weight
5 Marks
Find the median weight of the 30 students from the following distribution:
Weight (in kg) 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70
Number of students 2 5 8 6 6 3
Set 430/3/1
14. Single Missing Frequency \((f)\)
5 Marks
The mean weekly pocket allowance is ₹180. Find the value of \(f\), and then find the mode of the data:
Weekly Pocket Allowance (in ₹) 110 – 130 130 – 150 150 – 170 170 – 190 190 – 210 210 – 230 230 – 250
Number of Children 7 6 9 13 \(f\) 5 4
Set 430/3/2
15. Variable Class Frequencies
5 Marks
The total number of households is 25. Find the value of \(x\), then find the mean daily expenditure:
Daily Expenditure (in ₹) 500 – 750 750 – 1000 1000 – 1250 1250 – 1500 1500 – 1750
Number of Households 4 \(2x+1\) 12 \(x\) 2
Set 430/3/3
16. Mean and Mode – Combined
5 Marks
Find mean and mode of the following data:
Class 10 – 25 25 – 40 40 – 55 55 – 70 70 – 85 85 – 100
Number of Students 12 10 15 13 8 12
Set 430/5/1
17. Mode and Median – Hospital Data
5 Marks
Find mode and median of the ages of 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 7 10 21 22 15 5
Set 430/5/1