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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-12-MMM-01
Mean, Median & Mode (Grouped) — Assignment
Chapter: Statistics
Topic: Mean, Median, Mode of Grouped Data
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Mean of grouped data $=$
  • A.$\dfrac{\sum f_i x_i}{\sum f_i}$
  • B.$\sum f_i x_i$
  • C.middle value
  • D.mode
2.
The empirical relation is:
  • A.Mode $=3$ Median $-2$ Mean
  • B.Mean $=$ Mode
  • C.Median $=$ Mode
  • D.Mean $=$ Median
3.
The class with the highest frequency is the:
  • A.median class
  • B.modal class
  • C.mean class
  • D.open class
4.
The mid-value of a class is the:
  • A.frequency
  • B.class mark
  • C.cumulative frequency
  • D.mode
5.
The median is the:
  • A.most frequent value
  • B.average
  • C.middle value
  • D.range
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the mean of $2,4,6,8,10$.
7.
Find the mode of $2,3,3,4,5$.
8.
Find the median of $1,3,5,7,9$.
9.
If mean $=10$ and median $=12$, find the mode (empirical).
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Write the class marks of the classes $0$–$10$ and $10$–$20$.
11.
For data with $\sum f_i x_i=200$ and $\sum f_i=20$, find the mean.
12.
Find the median of $4,6,8,10,12,14$.
13.
If mode $=20$ and mean $=26$, find the median (empirical).
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the mean of the grouped data: classes $0$–$10,10$–$20,20$–$30,30$–$40$ with frequencies $2,3,4,1$.
15.
The mode of a distribution is $36$ and the mean is $30$. Using the empirical relation, find the median.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\dfrac{\sum f_i x_i}{\sum f_i}$
  2. (A) Mode $=3$ Median $-2$ Mean
  3. (B) modal class
  4. (B) class mark
  5. (C) middle value
Section B — Short Answer (2 marks)
  1. $6$.
  2. $3$.
  3. $5$.
  4. $16$.
Section C — Short Answer (3 marks)
  1. $5$ and $15$.
  2. $10$.
  3. $9$.
  4. $24$.
Section D — Long Answer (5 marks)
  1. $19$.
  2. $32$.
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