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Maths MCQ Class 11 Ch-15 | Statistics
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Mathematics
MCQ | Class 11 | Chapter 15
STATISTICS
Multiple Choice Questions (MCQ)
- MCQ Based on the Mean Deviation about Mean.
- MCQ Based on the Mean Deviation about Median.
- MCQ Based on the Variance and Standard Deviation of the given data.
Features
- In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.
- Solution Hints are also given to some difficult problems.
- Each MCQ contains four options from which one option is correct.
- On the right hand side column of the pdf Answer option is given.
Action Plan
- First of all students should Learn and write all basic points and Formulas related to the Statistics.
- Start solving the NCERT Problems with examples.
- Solve the important assignments on the Statistics Chapter 15 Class XI.
- Then start solving the following MCQ.
MCQ | CHAPTER 15 | CLASS 11
STATISTICS
Q 1) Find the mean deviation
about the median of the scores of a batsman given below
Innings |
1 |
2 |
3 |
4 |
5 |
6 |
Scores |
20 |
5 |
0 |
84 |
11 |
120 |
b)10.5
c) 11
d) 9.
Ans: b
Q 2) If mode of a series exceeds its mean by 12, then mode exceeds the median by:
a. 4
b. 8
c. 6
d. 10
(a) 121
(b) 11
(c) 12
(d) 21
117 |
156 |
206 |
198 |
223 |
b) 3
c) 1
d) 5
(a) 4
(b) 17
(c) 13
(d) 21
a. 5
b. 7
c. 4
d. 6
a) 153.5
b) 3.5
c) 155.25
d) 150
xi |
3 |
5 |
20 |
25 |
27 |
fi |
5 |
12 |
20 |
8 |
15 |
a) 7.7
b) 15
c) 8.7
d) 6.2
Ans: a
Q 9) If the mean of the following
data is 20.6, then the value of p is
X |
10 |
15 |
p |
25 |
35 |
F |
3 |
10 |
25 |
7 |
5 |
(b) 20
(c) 25
(d) 10
a) 71
b) 74
c) 70
d) 72
a. Median
b. Range
c. Mean
d. Mode
4.2 |
4.3 |
4 |
4.1 |
a) 0.27
b) 0.28
c) 0.3
d) 0.31
Ans: b
Q 13) If the standard deviation of a data is 0.012. Find the variance.
a) 0.144
b) 0.00144
c) 0.000144
d) 0.0000144
Ans: c
Q 14) When tested the lives (in hours) of 5 bulbs were noted as follows: 1357, 1090, 1666, 1494, 1623. The mean of the lives of 5 bulbs is
(a) 1445(b) 1446
(c) 1447
(d) 1448
Ans: b
Q 15) Find the variance of the first 10 natural numbers.
a) 7.25
b) 7
c) 8.25
d) 8
Ans: c
Q 16) The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be
a. 81
b. 36
c. 25
d. 57
Ans: a
Q 17) The algebraic sum of the deviation of 20 observations measured from 30 is 2. So, the mean of observations is
(a) 30.0
(b) 30.1
(c) 30.2
(d) 30.3
Ans: b
Solution Hint
Given, algebraic sum of of the deviation of 20 observations measured from 30 is 2
⇒ ∑(xi – 30) = 2 {1 ≤ i ≤ 20} ⇒ ∑xi – 30 × 20 = 2
⇒ (∑xi)/20 – (30 × 20)/20 = 2/20 ⇒ (∑xi)/20 – 30 = 0.1
⇒ Mean – 30 = 0.1 ⇒ Mean = 30 + 0.1 ⇒ Mean = 30.1
Q 18) Assuming the variance of four numbers w, x, y, and z as 9. Find the variance of 5w, 5x, 5y and 5z.
a) 225
b) 5/9
c) 9/5
d) 54
Ans: a
Now, h = (1/5). ⇒ Variance, (σu)2 = 9 × 25 = 225
(a) 20, 4
(b) 22, 6
(c) 22, 4
(d) 20, 6
Ans: c
Solution Hint
Again, the variance is independent of the change of origin. So it remains the same. Hence standard deviation also remain same.
a) Median will increase and S.D. will increase
b) Both will remain same
c) median will go up by 2 but S.D. will remain same
d) median will increase and S.D. will decrease
Ans: c
Solution Hint
a. mean
b. class size
c. frequency
d. mid-points
a) 4
b) 3
c) 2
d) 1
a) Origin
b) Scale
c) Origin and scale
d) Neither origin nor scale
Ans: a
Solution Hint Change in origin does not affect the standard deviation, whereas standard deviation is affected by scale.
a) 2.6
b) 2.8
c) 2.86
d) 3.24
a. 9
b. 33
c. 27
d. 17
a) 2, 6
b) 3, 3
c) 1, 5
d) 2, 4
a. 48
b. 15
c. 42
d. 45
(a) 18
(b) 20
(c) 22
(d) 24
Ans: b
Solution Hint
Now new mean is
∑ xi/100 = 1940/97 = 20
So, the new mean is 20
(a) 1/5
(b) 2/5
(c) 3/5
(d) 4/5
Ans: c
Solution Hint
Given, ∑x = 12 and ∑x² = 18
Now, variance = ∑x²/n – (∑x/n)²
⇒ variance = 18/10 – (12/10)²
⇒ variance = 9/5 – (6/5)²
⇒ variance = 9/5 – 36/25
⇒ variance = (9 × 5 – 36)/25
⇒ variance = (45 – 36)/25
⇒ variance = 9/25
⇒
Standard deviation = √(9/25)
Q 30) If the mean of first n natural numbers is 5n/9, then n =
(a) 5
(b) 4
(c) 9
(d) 10
Ans: c
Solution Hint
Given mean of first n natural number is 5n/9
⇒ (n+1)/2 = 5n/9
⇒ n + 1 = (5n×2)/9
⇒ n + 1
= 10n/9
⇒ 9(n + 1) = 10n
⇒ 9n + 9
= 10n
⇒ 10n – 9n = 9
a. 7
b. 8
c. 5
d. 10
a. 18
b. 19
c. 21
d. 20
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