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CBSE · Class 10 · Mathematics

Statistics

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
The class mark of the class 40–44 is:
  1. 46
  2. 44
  3. 4
  4. 42
2.
The mean of 80, 72, 85, 66, 40, 10, 88 is:
  1. 55.13
  2. 65
  3. 441
  4. 63
3.
For the data below, the modal class is:
Class: 15–20, 20–25, 25–30, 30–35, 35–40
Frequency: 17, 12, 8, 14, 10
  1. 15–20
  2. 30–35
  3. 20–25
  4. 25–30
4.
For the data below, the median class is:
Class: 80–100, 100–120, 120–140, 140–160, 160–180
Frequency: 12, 4, 19, 19, 11
  1. 140–160
  2. 120–140
  3. 80–100
  4. 100–120
5.
The class mark of the class 10–20 is:
  1. 30
  2. 10
  3. 15
  4. 20
6.
For a distribution, the mean is 43 and the median is 44. Using the empirical relation, the mode is about:
  1. 41
  2. 45
  3. 46
  4. 87
7.
Using the assumed mean method with a = 110, Σfi = 55 and Σfidi = 105, the mean is:
  1. 112.91
  2. 1.91
  3. 108.09
  4. 111.91
8.
Assertion (A): For the data below, the modal class is 50–60.
Class: 40–50, 50–60, 60–70, 70–80, 80–90, 90–100
Frequency: 15, 20, 17, 18, 18, 2
Reason (R): The class mark is the mid-point of a class.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Find the mean of this data. (Give your answer to 2 decimal places where needed.)
Class: 0–5, 5–10, 10–15, 15–20, 20–25
Frequency: 15, 17, 6, 17, 9
10.
Find the mode of this data. (Give your answer to 2 decimal places where needed.)
Class: 80–100, 100–120, 120–140, 140–160, 160–180, 180–200
Frequency: 14, 15, 8, 11, 10, 2
11.
Find the median of this data. (Give your answer to 2 decimal places where needed.)
Class: 5–10, 10–15, 15–20, 20–25, 25–30, 30–35
Frequency: 18, 17, 13, 8, 10, 17
12.
The mean of this data is 28.75. Find the missing frequency p.
Class: 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 7, p, 19, 3, 16
13.
Write the 'less than' cumulative frequency table for this data.
Class: 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 18, 8, 18, 6, 7
14.
Find the median of 59, 44, 64, 78, 63, 20, 59, 49.
15.
Find the mode of 33, 42, 21, 21, 22, 40, 27, 21.
16.
The mean of 8 numbers is 27. If one number, 77, is removed, find the mean of the remaining numbers. (Give your answer to 2 decimal places where needed.)
Section C — Word problems4 × 4 = 16 marks
17.
The marks of students in a test are shown below. Find the mean mark. (Give your answer to 2 decimal places where needed.)
Marks: 40–60, 60–80, 80–100, 100–120, 120–140
Number of students: 8, 9, 2, 4, 16
18.
The daily wages (in Rs) of workers in a factory are shown below. Find the median wage. (Give your answer to 2 decimal places where needed.)
Daily wage (Rs): 180–200, 200–220, 220–240, 240–260, 260–280, 280–300
Number of workers: 19, 7, 2, 13, 7, 13
19.
The ages (in years) of patients admitted to a hospital in a month are shown below. Find the mode. (Give your answer to 2 decimal places where needed.)
Age (years): 15–35, 35–55, 55–75, 75–95, 95–115
Number of patients: 5, 10, 19, 20, 8
20.
A survey counted the plants in each house of a locality. Find the mean number of plants per house. (Give your answer to 2 decimal places where needed.)
Number of plants: 0–2, 2–4, 4–6, 6–8, 8–10, 10–12
Number of houses: 18, 5, 4, 9, 4, 14
AmbifulWorksheets
Practice that never repeats
CBSE · Class 10 · Mathematics

Answer key

Statistics · AW-10M-STA-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 42(40 + 44) ÷ 2 = 42
2(d) 63441 ÷ 7 = 63
3(a) 15–20the highest frequency is 17
4(b) 120–140n = 65, n/2 = 32.5; cumulative frequencies 12, 16, 35, 54, 65
5(c) 15(10 + 20) ÷ 2
6(c) 46Mode = 3 Median − 2 Mean = 132 − 86
7(d) 111.91110 + (105 ÷ 55) = 111.91
8(b) Both A and R are true, but R is not the correct explanation of A.A is true: the highest frequency, 20, is in 50–60. R is true but does not explain A.
911.56class marks 2.5, 7.5, 12.5, 17.5, 22.5; Σfixi = 740, Σfi = 64
10102.5modal class 100–120: l = 100, f1 = 15, f0 = 14, f2 = 8, h = 20
1117.5n/2 = 41.5; median class 15–20: l = 15, cf = 35, f = 13, h = 5
12p = 3(Σfixi of the known classes + 15p) ÷ (45 + p) = 28.75
13less than 10: 18; less than 20: 26; less than 30: 44; less than 40: 50; less than 50: 57add the frequencies one class at a time
1459in order: 20, 44, 49, 59, 59, 63, 64, 78; the mean of the two middle values
152121 occurs 3 times, more than any other value
1619.86total = 8 × 27 = 216; (216 − 77) ÷ 7 = 19.86
1795.64Σfixi ÷ Σfi = 3730 ÷ 39
18Rs 243.85median = l + ((n/2 − cf) ÷ f) × h
1976.54 yearsmode = l + ((f1 − f0) ÷ (2f1 − f0 − f2)) × h
205.67class marks 1, 3, 5, 7, 9, 11; Σfixi ÷ Σfi = 306 ÷ 54