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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-12-CT
Statistics — Full Chapter Test
Chapter: Statistics
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
Cumulative frequency is the:
  • A.highest frequency
  • B.running total
  • C.class mark
  • D.range
3.
A histogram uses:
  • A.points
  • B.bars with no gaps
  • C.sectors
  • D.curves
4.
The empirical relation is:
  • A.Mode $=3$ Median $-2$ Mean
  • B.Mean $=$ Mode
  • C.Median $=$ Mode
  • D.Mean $=$ Median
5.
A "less than" ogive uses:
  • A.lower limits
  • B.upper class limits
  • C.class marks
  • D.frequencies
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the mean of $2,4,6,8,10$.
7.
For frequencies $3,5,7$, write the cumulative frequencies.
8.
Which graph is used for cumulative frequency?
9.
Find the mode of $2,3,3,4,5$.
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 classes $0$–$10,10$–$20,20$–$30$ with $f=4,6,10$, write the cumulative frequencies.
12.
State the difference between a bar graph and a histogram.
13.
For data with $\sum f_i x_i=200$ and $\sum f_i=20$, find the mean.
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.
Given less-than cumulative frequencies $<10:4,\ <20:10,\ <30:18,\ <40:24$, find the frequency distribution and $N$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\dfrac{\sum f_i x_i}{\sum f_i}$
  2. (B) running total
  3. (B) bars with no gaps
  4. (A) Mode $=3$ Median $-2$ Mean
  5. (B) upper class limits
Section B — Short Answer (2 marks)
  1. $6$.
  2. $3,8,15$.
  3. The ogive.
  4. $3$.
Section C — Short Answer (3 marks)
  1. $5$ and $15$.
  2. $4,10,20$.
  3. A bar graph has gaps (categorical); a histogram has no gaps (continuous data).
  4. $10$.
Section D — Long Answer (5 marks)
  1. $19$.
  2. Frequencies $4,6,8,6$; $N=24$.
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