Vidaara.orgClass 11 · Mathematics
CodeVID-M11-13-SD-01
Variance & Standard Deviation — 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.
Standard deviation $=$
- A.variance$^2$
- B.$\sqrt{\text{variance}}$
- C.$\tfrac{1}{\text{variance}}$
- D.mean
2.
Variance $=$
- A.$\tfrac1n\sum(x_i-\bar x)^2$
- B.$\tfrac1n\sum(x_i-\bar x)$
- C.$\max-\min$
- D.$\sqrt{n}$
3.
The SD of a constant data set is:
- A.the constant
- B.$0$
- C.$1$
- D.undefined
4.
Variance is always:
- A.negative
- B.$\ge0$
- C.$<0$
- D.$=1$
5.
If each value increases by $5$, the variance:
- A.increases by $5$
- B.stays the same
- C.increases by $25$
- D.doubles
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the mean of $2,4,6,8,10$.
7.
Find the variance of $2,4,6$.
8.
Find the SD of $4,4,4,4$.
9.
Find the variance of $1,2,3$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the variance and SD of $6,8,10,12,14$.
11.
Find the SD of $2,4,6,8,10$.
12.
Find the variance of the first $5$ natural numbers.
13.
Find the variance of $3,5,7,9,11$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the mean and standard deviation of $6,7,10,12,13,4,8,12$.
15.
The variance of $20$ observations is $5$. If each observation is multiplied by $2$, find the new variance.
Answer Key
Section A — Multiple Choice Questions
- (B) $\sqrt{\text{variance}}$
- (A) $\tfrac1n\sum(x_i-\bar x)^2$
- (B) $0$
- (B) $\ge0$
- (B) stays the same
Section B — Short Answer (2 marks)
- $6$.
- $\tfrac83$.
- $0$.
- $\tfrac23$.
Section C — Short Answer (3 marks)
- Variance $8$, SD $2\sqrt2$.
- $2\sqrt2$.
- $2$.
- $8$.
Section D — Long Answer (5 marks)
- Mean $9$, variance $9.25$, SD $\approx3.04$.
- $20$.
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