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CBSE · Class 11 · Social Science

Measures of Central Tendency

Standard difficulty · 20 questions · 40 marks · Time: 38 minutes

Name: Date: Score: ____ / 40

Write full answers in 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 sum of observations divided by their number is the:
  1. mode
  2. range
  3. median
  4. arithmetic mean
2.
Find the arithmetic mean of 86, 89, 81, 63, 83, 84.
  1. 81
  2. 82
  3. 486
  4. 89
3.
Find the median of 10, 88, 20, 24, 46, 22, 67.
  1. 49
  2. 39.57
  3. 25
  4. 24
4.
What is the mode of 30, 53, 26, 53, 53, 30, 32, 35, 23?
  1. 32
  2. 53
  3. 30
  4. 26
5.
Find the mean of this discrete series.
Value (X): 100, 120, 140, 160, 180
Frequency (f): 6, 2, 15, 13, 7
  1. 146.05
  2. 1,256
  3. 140
  4. 148.05
6.
The mean of 4 observations is 75. 3 of them are 61, 84, 80. What is the missing observation?
  1. 79
  2. 300
  3. 76
  4. 75
7.
A student scores 65, 98 and 73 in three tests carrying weights 3, 4, 5. What is the weighted mean mark?
  1. 78.67
  2. 79.33
  3. 82.33
  4. 317.33
8.
In ordered data of 43 items, the median is the size of which item?
  1. 23th
  2. 10.75th
  3. 22th
  4. 21.5th
Section B — Short answer8 × 2 = 16 marks
9.
What is a measure of central tendency?
10.
Find the mean of 65, 59, 47, 50, 29 by the assumed mean method, taking A = 60. Show Σd.
11.
Find the median of this distribution.
Class: 30–35, 35–40, 40–45, 45–50, 50–55
Frequency: 30, 5, 22, 24, 16
12.
Find the mode of this distribution.
Class: 40–60, 60–80, 80–100, 100–120, 120–140
Frequency: 19, 27, 22, 18, 24
13.
Find the median of this discrete series.
Value: 40, 50, 60, 70, 80
Frequency: 8, 5, 6, 15, 6
14.
Find Q3 of 14, 29, 68, 72, 76, 86, 93 (already in order).
15.
Find the mean of this distribution by the direct method (use class marks).
Class: 20–30, 30–40, 40–50, 50–60, 60–70
Frequency: 24, 17, 16, 18, 26
16.
A candidate is at the 86th percentile among 116,000 candidates. About how many scored above the candidate, and what share is that?
Section C — Longer answers4 × 4 = 16 marks
17.
Compare the mean, median and mode.
18.
Daily wages of workers are given below. (a) Find the mean wage (use class marks). (b) Find the median wage. (c) Which is higher here?
Daily wage (₹): 100–120, 120–140, 140–160, 160–180, 180–200
Workers: 3, 28, 11, 12, 16
19.
Find the mean of this distribution by the step deviation method, taking A = 55 and c = 10. Show Σfd′.
Class: 30–40, 40–50, 50–60, 60–70, 70–80
Frequency: 24, 24, 27, 18, 10
20.
Five families earn ₹13,000, ₹8,500, ₹12,500, ₹13,500, ₹100,000 a month. (a) Find the mean. (b) Find the median. (c) Which better shows a typical family’s income, and why?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 11 · Social Science

Answer key

Measures of Central Tendency · AW-11SS-ECT-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) arithmetic mean—
2(a) 81486 ÷ 6 = 81
3(d) 24in order: 10, 20, 22, 24, 46, 67, 88; the middle value
4(b) 5353 occurs 3 times, more than any other value
5(a) 146.05Σfx ÷ Σf = 6,280 ÷ 43
6(d) 754 × 75 − 225 = 75
7(b) 79.33(65 × 3 + 98 × 4 + 73 × 5) ÷ 12
8(c) 22th(N + 1) ÷ 2 with N = 43
9A single value that represents a whole set of data, such as the mean, median or mode.—
10Σd = −50; mean = 50d = X − 60; mean = 60 + Σd ÷ 5
1143.07N ÷ 2 = 48.5; median class 40–45: L = 40, c.f. = 35, f = 22, h = 5
1272.31modal class 60–80: L = 60, D1 = 8, D2 = 5, h = 20; L + D1 ÷ (D1 + D2) × h
1370(N + 1) ÷ 2 = 20.5; cumulative frequencies 8, 13, 19, 34, 40
14863(N + 1) ÷ 4 = 6th item: item 6
1545.50Σfm ÷ Σf = 4,595 ÷ 101
16about 16,240, 14%(100 − 86)% of 116,000
17The mean uses all values but is pulled by extremes; the median is the middle value and resists extremes; the mode is the most frequent value and suits the most typical size or choice.—
18(a) ₹152.86 (b) ₹147.27 (c) the meanmean = Σfm ÷ Σf; median = L + ((N ÷ 2 − c.f.) ÷ f) × h
19Σfd′ = −34; mean = 51.70d′ = (m − 55) ÷ 10; mean = A + (Σfd′ ÷ Σf) × c
20(a) ₹29,500 (b) ₹13,000 (c) the median, because the mean is pulled up by one very high income147,500 ÷ 5; middle value in order