Class 11 Mathematics Statistics MCQs Set E

Question: When tested, the lives (in hours) of 5 bulbs were noted as follows 1357, 1090, 1666, 1494, 1623 The mean deviations (in hours) from their mean is
(a) 178
(b) 179
(c) 220
(d) 356 
Answer: a

Question: Coefficient of skew ness for the values Median = 18 8. , Q₁ = 14 6. , Q₃ = 252. is
(a) 0.2
(b) 0.5
(c) 0.7
(d) None of these 
Answer: a

Question: If two variables x y and are such that 2y+5=3x and Quartile Deviation (QD) of x is 8, then (QD) of y is
(a) 2
(b) 8
(c) 4
(d) None of these 
Answer: d

Question: The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is 
(a) 2
(b) 2.57
(c) 3
(d) 3.75 
Answer: b

Question: The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
(a) 40%
(b) 20%
(c) 80%
(d) 60% 
Answer: c

Question: The mean of the numbers a, b, 8, 5 10 is 6 and the variance is 6.80. Then, which one of the following gives possible values of a b and ? 
(a) a =3, b=4
(b) a = 0, b=7
(c) a = 5, b=2
(d) a = 1, b= 6 
Answer: a

Question: Coefficient of variation of two distributions are 50 and 60 and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is
(a) 0
(b) 1
(c) 1.5
(d) 2.5 
Answer: a

Question: The SD of 15 items is 6 and if each item is decreases by 1, then standard deviation will be
(a) 5
(b) 7
(c) 91/15
(d) 6 
Answer: d

Question: If x̅ is the arithmetic mean of n independent variates x₁,x₂,x₃,…,x_n each of the standard deviation s, then variance (x̅ ) is
(a) σ²/n
(b) n σ²
(c) (n+1 )σ²/3
(d) None of these
Answer: a

Question: Median of ²ⁿCo,²ⁿC1,²ⁿC_2,²ⁿC_{3,…,²ⁿCn} (where, n is even) is
(a) 2nCn/2
(b) 2nCn+1/2
(c) 2nCn-1/2
(d) None of these 
Answer: a

Question: If in a moderately asymmetrical distribution mode and mean of the data are 6l and 9l respectively, then median is
(a) 8λ
(b) 7λ
(c) 6λ
(d) 5λ 
Answer: a

Question: The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is 
(a) 50000
(b) 250000
(c) 252500
(d) 255000 
Answer: c

Question: Let x₁,x₂,x₃,x₄ and x₅ and be the observations with mean m and standard deviation S. The standard deviation of the observations kx₁, kx₂, kx₃, kx₄  and is kx₅ is
(a) k+5
(b) S/k
(c) k S
(d) S 
Answer: c

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

Question: Standard deviations for first 10 natural numbers is
(a) 5.5
(b) 3.87
(c) 2.97
(d) 2.87 
Answer: d

Question: Let x₁,x₂,..,x_n be n observations. Let w_i = l+_i +k for i=1,2,…,n, n = 1 2, , …, , where l and k are constants. If the mean of x_i‘s is 48 and their standard deviation is 12, the mean of w _i ’s is 55 and standard deviation of w _i ’s is 15, the values of l k and should be
(a) l = 1.25 ,k = -5
(b) l = – 1.25, k = 5
(c) l = 2.5, k = -5
(d) l = 2.5 k = 5 
Answer: a

Question: If a variable takes the discrete values α + 4 , α -7/2,α-5/2,α-3, α-2,α+1/2, α+5(α>0), 5/2, α-3, α-1/2 ,then the median is
(a) α – 5/4
(b) α – 1/2
(c) α – 2
(d) α +5/4
Answer: a

Question: If 5 is added in each observation, then the new variance is
(a) σ²
(b) σ² + 5
(c) σ²-5
(d) None of these 
Answer: a

Question: If xi is replaced by xi’, then new mean is
(a) x̅ – xi + xi’ 
(b)(n-1) x̅ + x_i‘
(c) n x̅ – xi + xi /n
(d) None of these 
Answer: c

Question: If the mode of the data is 18 and the mean is 24, then median is
(a) 18
(b) 24
(c) 22
(d) 21 
Answer: a

Question: Let a, b, c, d e and e be the observations with mean m and standard deviation S. The standard deviation of the observations a+ k, b+ k c+ k ,d +k, e+ k is
(a) S
(b) k S
(c) S +k
(d) S/k 
Answer: a

Question: The following information relates to a sample of size 60 : ∑x2 = 18000, ∑x= 960. 
The variance is
(a) 6.63
(b) 16
(c) 22
(d) 44 
Answer: d

Question: The mean and variance of n values of a variable x are 0 and σ2 , respectively. If the variable y =x² , then mean of y is
(a) σ
(b) σ²
(c) 1
(d) None of these 
Answer: b

Question: Find the mean deviation about the mean of the set of first n natural numbers when n is an odd number.
(a) n²+1/4n
(b) n²-1/4n
(c) n²-3/5n
(d) None of these 
Answer: b

Question: The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is 
(a) √52/7
(b) 52/7
(c) 6
(d) 6 
Answer: a

Question: Which of the following is a correct statement?
(a) The sum of the deviations from arithmetic mean is zero
(b) Computation of arithmetic mean is based on all observations
(c) It gives no importance to extreme values
(d) None of the above
Answer: a,b

Question: For two data sets, each of size 5, the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is 
(a) 5/2
(b) 11/2
(c) 6
(d) 13/2 
Answer: b

Question: Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, then variance of the numbers so obtained is
(a) 6.5
(b) 2.87
(c) 3.87
(d) 8.25 
Answer: d

Question: If the mean deviations about the median of the numbers a, 2a,…,5a is 50, then |a| is equal to
(a) 3
(b) 4
(c) 5
(d) 2 
Answer: b

Question: For a series the value of mean deviation is 15, the most likely value of its quartile deviation is
(a) 12.5
(b) 11.6
(c) 13
(d) 9.7 
Answer: a

Question: Following are the marks obtained by 9 students in a Mathematics test 50, 69, 20, 33, 53, 39, 40, 65, 59 The mean deviation from the median is
(a) 9
(b) 10.5
(c) 12.67
(d) 14.76 
Answer: c

Question: If the mean deviation of number 1,1+d,1+2d,…1 +10d from their mean is 255,then the d is equal to
(a) 10.0
(b) 20.0
(c) 10.1
(d) 20.2
Answer: c

Question: If the median of 21 observations is 40 and if the observations greater than the median are increased by 5, then the median of the new data will be
(a) 40
(b) 45
(c) 4+50/21
(d) 45-50/21 
Answer: a

Question: In a moderately skewed distribution the values of mean and median are 5 and 6, respectively. The value of mode in such a situation is approximately equal to
(a) 8
(b) 11
(c) 16
(d) None of these 
Answer: a

Question: If the sum of 11 consecutive natural numbers is 2761, then the middle number is
(a) 249
(b) 250
(c) 251
(d) 252
Answer: c

Question: The quartile deviation of daily wages (in R.s.) of 7 persons given below 12, 7, 15, 10, 17, 19 and 25 is
(a) 14.5
(b) 5
(c) 9
(d) 4.5 
Answer: d

Question: Consider the following statements I. The values of median and mode can be determined graphically.
II. Mean, median and mode have the same unit.
III. Range is the best measure of dispersion.
Which of these is/are correct?
(a) Only I
(b) Only II
(c) Both II and III
(d) None of these 
Answer: a

Assertion and Reason

Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

Question: Suppose two groups of scores A and B are such that A = (+, x+2, x+4) and B= (x-2, x+2, x+6)
Statement I Group B has more variability than group A.
Statement II The value of mean for group B is more than that of group A. 
Answer: c

Question: If n is a natural number, then 
Statement I The mean of the squares of first n natural number is (n+1)(2n+1)/6.
Statement II ∑n = n(n+1)/2
Answer: b

Question: Statement I If μ is the mean of a distribution, then ∑fi (yi-μ ) is equal to 0.
Statement II The mean of the square of first n natural numbers is 1/6 n(2n+1). 
Answer: c

Question: Statement I The variance of first n natural numbers is n2-1/12..
Statement II The sum of first n natural numbers is n(n +1)/2 and the sum of squares of first n natural numbers is n(n+1) (2n+1/6 
Answer: a

Question. Karl-Pearson’s coefficient of skewness of a distribution is 0.32. Its S.(d) is 6.5 and mean 39.6. Then the median of the distribution is given by:     
(a) 28.61
(b) 38.81
(c) 29.13
(d) 28.31

Answer: B

Question. Maximize z = 3x + 2y, subject to x + y ≥1, y − 5x ≤ 0, x − y ≥ −1, x + y ≤ 6, x ≤ 3 and x, y ≥ 0 
(a) x = 3
(b) y = 3
(c) z =15
(d) All the above

Answer: D

Question. Maximum value of 4x + 5y subject to the constraints x + y ≤ 20, x + 2y ≤ 35, x − 3y ≤12 is     
(a) 84
(b) 95
(c) 100
(d) 96

Answer: B

Question. The maximum value of μ = 3x + 4y subjected to the conditions x + y ≤ 40, x + 2y ≤ 60; x, y ≥ 0 is     
(a) 130
(b) 120
(c) 40
(d) 140

Answer: D

Question. z = ax + by,a,b being positive, under constraints y ≥1, x − 4y + 8 ≥ 0, x, y ≥ 0 has:      
(a) Finite maximum
(b) Finite minimum
(c) An unbounded minimum solution
(d) An unbounded maximum solution

Answer: B,D

Question. A, B, C, D are non-zero constants, such that       
(a) both A and C are negative.
(b) A and C are of opposite sign.
If coefficient of correlation between x and y is r, then that between AX + B and CY + D is
(a) r 
(b) –r
(c) A/(c)r
(d) –A/(c)r

Answer: A,B

Question. Karl-Pearson’s coefficient of skewness of a distribution is 0.32. Its S.(d) is 6.5 and mean 39.6. Then the median of the distribution is given by:       
(a) 28.61
(b) 38.81
(c) 29.13
(d) 28.31

Answer: B

Question. Given that the regression coefficients are – 1.5 and – 0.5, the value of the correlation coefficient is:   
(a) 0.75
(b) 0.7
(c) – 0.87
(d) – 0.5

Answer: C

Question. The solution of set of constraints x + 2 y ≥ 11, 3x + 4 y ≤ 30, 2x + 5 y ≤ 30, x ≥ 0, y ≥ 0 includes the point:     
(a) (2, 3)
(b) (3, 2)
(c) (3, 4)
(d) (4, 3)

Answer: C

Question. The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be:     
(a) 40
(b) 45
(c) 40 + 21/25
(d) None of these

Answer: A

Assertion and Reason
Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
e. If assertion is false but reason is true.

Question. Assertion: The variance of first n even natural numbers is = (n+1)(n-1)/3 = n²–1/3 ?       
Reason: Arithmetic mean and the variance are same.

Answer: B

Question. The graph of x ≤ 2 and y ≥ 2 will be situated in the:       
(a) First and second quadrant
(b) Second and third quadrant
(c) First and third quadrant
(d) Third and fourth quadrant

Answer: A

Question. Let x₁ , x₂,...., x_n be n observations, and let x be their arithmetic mean and σ2 be the variance?       
Assertion: Variance of 2x₁ , 2x₂......2x_n is 4σ² .
Reason: Arithmetic mean 2x₁ , 2x₂......2x_n is x̅.

Answer: C