CBSE Class 11 Mathematics Chapter 15 Statistics Multiple Choice Questions with Answers. MCQ Class 11 Mathematics Statistics with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 11 Mathematics Statistics MCQs with Answers to know their preparation level.
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MCQ Class 11 Mathematics Statistics with Answers - Set - 2
Question 1:
Let x1, x2, x3, ……… , xn, be n observations and X be the arithmetic mean. Then formula for the standard deviation is given by
(a) ∑(xi – mean)²
(b) ∑(xi – mean)2 /n
(c) √{∑(xi – mean)²/n}
(d) None of these
Correct Answer – (C)
Given, x1, x2, x3, ………. , xn be n observations and X be the arithmetic mean.
Now standard deviation = √{∑(xi – mean)²/n}
Question 2 :
The mean of a group of 100 observations was found to be 20. Later on, it was found that three observations were incorrect, which was recorded as 21, 21 and 18. Then the mean if the incorrect observations are omitted is
(a) 18
(b) 20
(c) 22
(d) 24
Correct Answer – (B)
Given mean of 100 observations is 20
Now
∑ xi/100 = 20 (1 = i = 100)
⇒ ∑xi = 100×20
⇒ ∑xi = 2000
3 observations 21, 21 and 18 are recorded in-correctly.
So ∑xi = 2000 – 21 – 21 – 18
⇒ ∑xi = 2000 – 60
⇒ ∑xi = 1940
Now new mean is
∑ xi/100 = 1940/97 = 20
So, the new mean is 20
Question 3 :
If a variable takes discrete values x + 4, x – 7/2, x – 5/2, x – 3, x – 2, x + 1/2, x – 1/2, x + 5 (x > 0), then the median is
(a) x – 5/4
(b) x – 1/2
(c) x – 2
(d) x + 5/4
Correct Answer – (A)
Given, discrete values x + 4, x – 7/2, x – 5/2, x – 3, x – 2, x + 1/2, x – 1/2, x + 5
Now, arrange them in ascending order, we get
x – 7/2, x – 3, x – 5/2, x – 2, x – 1/2, x + 1/2, x + 4, x + 5
Total observations = 8
Now, median = AM of 4th and 5th observations
= AM of (x – 2) and (x – 1/2) observations
= (x – 2 + x – 1/2)/2
= (2x – 5/2)/2
= x – 5/4
Question 4 :
If one of the observation is zero then geometric mean is
(a) (Sum of observation)/n
(b) (Multiplication of all observations)n
(c) (Multiplication of all observations)1/n
(d) 0
Correct Answer – (D)
Let the observations are 0, a, b, c, ……… up to n
Now, geometric mean = (0 × a × b × c × ……… up to n)1/n
= 0
So, geometric mean is 0
Question 5 :
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
(a) 30
(b) 20
(c) 25
(d) 10
Correct Answer – (B)
Mean = ∑ f i× x i /∑ f i
⇒ 20.6 = (10 × 3 + 15 × 10 + p × 25 + 25 × 7 + 35 × 5)/(3 + 10 + 25 + 7 + 5)
⇒ 20.6 = (30 + 150 + 25p + 175 + 175)/50
⇒ 20.6 = (530 + 25p)/50
⇒ 530 + 25p = 20.6 × 50
⇒ 530 + 25p = 1030
⇒ 25p = 1030 – 530
⇒ 25p = 500
⇒ p = 500/25
⇒ p = 20
So, the value of p is 20
MCQ Class 11 Mathematics Statistics with Answers
Question 6 :
Variance is independent of change of
(a) origin only
(b) scale only
(c) origin and scale both
(d) None of these
Correct Answer – (A)
Variance is independent of change of origin only.
Question 7 :
If covariance between two variables is 0, then the correlation coefficient between them is
(a) nothing can be said
(b) 0
(c) positive
(d) negative
Correct Answer – (B)
The relationship between the correlation coefficient and covariance for two variables as shown below:
r(x, y) = COV(x, y)/{sx × sy}
r(x, y) = correlation of the variables x and y
COV(x, y) = covariance of the variables x and y
sx = sample standard deviation of the random variable x
sx = sample standard deviation of the random variable y
Now given COV(x, y) = 0
Then r(x, y) = 0
Question 8 :
Which one is measure of dispersion method
(a) Range
(b) Quartile deviation
(c) Mean deviation
(d) all of the above
Correct Answer – (D)
Range, Quartile deviation, Mean deviation all are the measure of dispersions method.
Question 9 :
If the mean of first n natural numbers is 5n/9, then n =
(a) 5
(b) 4
(c) 9
(d) 10
Correct Answer – (C)
Question 10 :
If the variance of the data is 121 then the standard deviation of the data is
(a) 121
(b) 11
(c) 12
(d) 21
Correct Answer – (B)
Given, variance of the data = 121
Now, the standard deviation of the data = √(121) = 11
- NCERT Solutions Class 11 Mathematics Statistics with Answers : Exercise 15.1
- NCERT Solutions Class 11 Mathematics Statistics with Answers : Exercise 15.2
- NCERT Solutions Class 11 Mathematics Statistics with Answers : Exercise 15.3
- NCERT Solutions Class 11 Mathematics Statistics with Answers : Exercise 15 Misc
- NCERT Solutions Class 11 Mathematics Textbook download
