Vidaara.orgClass 11 · Mathematics
CodeVID-M11-13-CV-01
Coefficient of Variation — Assignment
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.
CV $=$
- A.$\dfrac{\sigma}{\bar x}\times100$
- B.$\dfrac{\bar x}{\sigma}\times100$
- C.$\sigma\bar x$
- D.$\sigma+\bar x$
2.
The series with the higher CV is:
- A.more consistent
- B.more variable
- C.equal
- D.smaller
3.
The CV is measured in:
- A.units of data
- B.percent
- C.square units
- D.degrees
4.
To compare consistency we use:
- A.range
- B.CV
- C.mode
- D.sum
5.
Lower CV means the data is:
- A.more variable
- B.more consistent
- C.larger
- D.negative
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the CV if mean $=50$ and SD $=5$.
7.
Find the CV if mean $=20$ and SD $=4$.
8.
Which is more consistent: CV $12\%$ or CV $18\%$?
9.
If mean $=40$ and CV $=25\%$, find the SD.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Series A has mean $60$, SD $6$; series B has mean $80$, SD $12$. Find both CVs and state which is more consistent.
11.
The mean of a series is $25$ and the SD is $5$. Find the CV.
12.
If CV $=40\%$ and SD $=8$, find the mean.
13.
A data set has mean $100$ and variance $64$. Find the CV.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Batsman A: mean $50$, SD $5$; batsman B: mean $40$, SD $6$. Determine who is more consistent.
15.
For data with mean $18$ and variance $36$, find the CV; then find the new CV if every value is increased by $4$.
Answer Key
Section A — Multiple Choice Questions
- (A) $\dfrac{\sigma}{\bar x}\times100$
- (B) more variable
- (B) percent
- (B) CV
- (B) more consistent
Section B — Short Answer (2 marks)
- $10\%$.
- $20\%$.
- $12\%$ (lower CV).
- $10$.
Section C — Short Answer (3 marks)
- A: $10\%$, B: $15\%$; A is more consistent.
- $20\%$.
- $20$.
- $8\%$.
Section D — Long Answer (5 marks)
- A (CV $10\%$) is more consistent than B (CV $15\%$).
- Original CV $\approx33.33\%$; new CV $\approx27.27\%$.
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