Class 11 Mathematics Statistics MCQs Set 03

Question: The mean age of a combined group of men and women is 30 years. If the means of the age of men and women are respectively 32 and 27, then the percentage of women in the group is:
a) 30
b) 40
c) 50
d) 60
Answer: b

Question: The mean deviation of the numbers 3, 4, 5, 6, 7 is:
a) 0
b) 1.2
c) 5
d) 25
Answer: b

Question: The variance of the first n natural numbers is:
a) n²–1/12
b) n²–1/6
c) n²+1/6
d) n²+1/12
Answer: a

Question: Let x₁ , x₂ ,x₃….. x_n be n observations such that ∑x₁² = 400 and ∑xi = 80 . Then a possible value of n among the following is:
a) 9
b) 12
c) 15
d) 18
Answer: d

Question: The weighted mean of first n natural numbers whose weights are equal to the squares of corresponding numbers is:
a) n+1/2
b) 3n(n+1)/2(n+1)
c) (n+1)(2n+1)/6
d) n(n+1)/2
Answer: b

Question: If the mean of 3, 4, x, 7, 10 is 6, then the value of x is:
a) 4
b) 5
c) 6
d) 7
Answer: c

Question: The mean of 5 numbers is 18. If one number is excluded, their mean becomes 16. Then the excluded number is:
a) 18
b) 25
c) 26
d) 30
Answer: c

Question: If Var(x) = 8.25, Var(y) = 33.96 and Cov (x,y) = 10.2, then the correlation coefficient is:
a) 0.89
b) – 0.98
c) 0.61
d) – 0.16
Answer: c

Question: The two regression lines are 2x −9y +6=0 and x−2y+1=0 . What is the correlation coefficient between x and y
a) –2/3
b) 2/3
c) 4/9
d) None of the options
Answer: b

Question: For a symmetrical distribution Q1 = 25 and Q3 = 45, the median is:
a) 20
b) 25
c) 35
d) None of the options
Answer: c

Question: If the mean of the set of numbers x₁ x₂ x₃….. x_n is X̅ then the mean of the numbers x1 + 2i , 1≤i≤n is :
a) X̅ + 2n
b) X̅ + n+1
c) X̅ + 2
d) X̅ + n
Answer: b

Question: The median of 10, 14, 11, 9, 8, 12, 6 is:
a) 10
b) 12
c) 14
d) 11
Answer: a

Question: Variance of the numbers 3, 7, 10,18, 22 is equal to
a) 12
b) 6.4
c) 49.2
d) 49.2
Answer: d

Question: Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is:
a) 48
b) 82x 1/2
c) 50
d) 80
Answer: c

Question: The two lines of regression are given by 3x + 2y = 26 and 6x + y = 31 . The coefficient of correlation between x and y is
a) -1/3
b) 1/3
c) -1/2
d) 1/2
Answer: c

Question: The mode of the distribution:

a) 5
b) 6
c) 8
d) 10
Answer: b

Question: If the mean of the distribution is 2.6, then the value of y is:

a) 24
b) 13
c) 8
d) 3
Answer: c

Question: Karl Pearson’s coefficient of correlation between the heights (in inches) of teachers and students corresponding to the given data is:

a) 1/√2
b) √2
c) -1/√2
d) 0
Answer: a

Question: The upper quartile for the following distribution is given by the size of:

Answer: c

Question: Karl Pearson’s coefficient of correlation between x and y for the following data is:

a) 0.480
b) – 0.480
c) 0.408
d) – 0.408
Answer: c

Question: If two random variables x and y, are connected by relationship 2x + y = 3, then xy r =
a) 1
b) – 1
c) – 2
d) 3
Answer: b

Question: In-equations 3x − y ≥ 3 and 4x − y > 4
a) Have solution for positive x and y
b) Have no solution for positive x and y
c) Have solution for all x
d) Have solution for all y
Answer: a

Question: The coefficients of correlation between the heights (in inches) of fathers and sons from the following data will be:

a) 0.60
b) – 0.60
c) – 0.67
d) 0.67
Answer: d

Question: For the following data ∑(x–x̅)2= 36, ∑(y–y̅)2 = 256 , (x–x̅)(y–y̅) = 80 The Pearson’s coefficient of correlation is:
a) 0.2
b) 0.01
c) 1
d) 0.1
Answer: c

Question: di is the deviation of a class mark yi from ‘a’ the assumed mean and fi is the frequency, IF

a) Lower limit
b) Assumed mean
c) Number of observations
d) Class size
Answer: b

Question: The harmonic mean of 3, 7, 8, 10, 14 is:

Answer: d

Question: Find the mode from the data given below:
Marks obtained   0 – 5   5 – 10   10 – 15   15 – 20   20 – 25   25 – 30
No. of students    18         20           25           30           16           14
a) 16.1
b) 16.2
c) 16.7
d) 16.3
Answer: d

Question: Consider the frequency distribution of the given numbers

If the mean is known to be 3, then the value of f is:
a) 3
b) 7
c) 10
d) 14
Answer: d

Question: Consider the following statements :
a) Mode can be computed from histogram
b) Median is not independent of change of scale
c) Variance is independent of change of origin and scale.
Which of these is / are correct ?
a) (a), b) and (c)
b) only (b)
c) only (a) and (b)
d) only (a)
Answer: c