Class 11 Mathematics Statistics MCQs Set 02

Question: Coefficient of variation of two distribution are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic means?
a) 35, 22.85
b) 22.85, 35.28
c) 36, 22.85
d) 35.28, 23.85
Answer: a

Question: If regression coefficient of y on x is 8/5 and that of x on y is 2/5 and the acute angle between the two lines is α , then the value of tan α is:
a) 9/25
b) 9/2√5
c) 3/25
d) 9/50
Answer: d

Question: If x represents the mean of n observations x₁,x₂, ………, x_n, then value of
a) –1
b) 0
c) 1
d) n – 1
Answer: a

Question: The marks obtained by 60 students in a certain test are given below :
Mean and Median of the above data are respectively
a) 64.33, 68.33
b) 60, 70
c) 66.11, 71.11,
d) None of the options
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: If you want to measure the intelligence of a group of students,which one of the following measures will be more suitable?
a) Arithmetic mean
b) Mode
c) Median
d) Geometric mean
Answer: d

Question: If mean of the n observations x₁, x₂, x₃,… x_n be x– , then the mean of n observations 2x₁ + 3, 2x₂ + 3, 2x₃ + 3, …., 2x_n + 3 is
a) 3x + 2
b) 2x + 3
c) x + 3
d) 2x
Answer: b

Question: The measure of dispersion is:
a) mean deviation
b) standard deviation
c) quartile deviation
d) all of the options
Answer: d

Question: The variance of first n natural numbers is :
a) n²+1 / 12
b) (n + 1)(2n + 1) /6
c) n²+n / 12
d) n²-1 / 12
Answer: d

Question: The definition of Mode fails if:
a) the maximum frequency is repeated
b) the maximum frequency is not repeated
c) the maximum frequency occurs in the middle
d) the curve drawn with the help of given data is symmetrical
Answer: b

Question: In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?
a) 73
b) 65
c) 68
d) 74
Answer: b

Question: A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s and seven 10’s. The mode of this set of numbers is
a) 6
b) 7
c) 8
d) 10
Answer: c

Question: Mean score of six students in an examination is 48. If the individual scores of five students be 45, 58, 50, 54 and 49, then the score of the sixth student is equal to:
a) 32
b) 34
c) 40
d) 42
Answer: a

Question: The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set
a) remains the same as that of the original set
b) is increased by 2
c) is decreased by 2
d) is two times the original median.
Answer: a

Question: If the arithmetic mean of the numbers x1 x2 x3….. xn is X̅ , then the arithmetic mean of numbers ax1 + b)x2 b)x3+b,…… axn + b , where a, b are two constants would be
a) x̅
b) nax̅+nb
c) ax̅
d) ax̅ + b
Answer: d

Question: Mean of 20 observations is 15.5 Later it was found that the observation 24 was misread as 42. The corrected mean is:
a) 14.2
b) 14.8
c) 14.0
d) 14.6
Answer: d

Question: The observation which occur most frequently is known as :
a) mode
b) median
c) weighted mean
d) mean
Answer: a

Question: If the mean of n observations 12, 22, 32….,n2 is 46n /,11 then n is equal to
a) 11
b) 12
c) 23
d) 22
Answer: a

Question: The reciprocal of the mean of the reciprocals of n observation is the :
a) geometric mean
b) median
c) harmonic mean
d) average
Answer: c

Question: If the values of regression coefficients are – 0.33 and –1.33, then the value of coefficient of correlation between the two variables, is
a) 0.2
b) – 0.66
c) 0.4
d) – 0.4
Answer: b

Question: If the mean of four observations is 20 and when a constant c is added to each observation, the mean becomes 22. The value of c is :
a) – 2
b) 2
c) 4
d) 6
Answer: b

Question: A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s and seven 10’s. The mode of this set of numbers is:
a) 6
b) 7
c) 8
d) 10
Answer: c

Question: The G.M. of the numbers 3, 32 ,33 ,….. 3n is:
a) 32/n
b) 3(n-1)/2
c) 3n/2
d) 3(n+1)/2
Answer: d

Question: If the lines of regression be x − y = 0 and 4x − y − 3 = 0 ,and 2 1, x σ = then the coefficient of correlation is
a) – 0.5
b) 0.5
c) 1.0
d) – 1.0
Answer: b

Question: The standard deviation of 35, 40, 42, 36, 27 :
a) 25.8
b) 26.9
c) 26.8
d) 27.8
Answer: c

Question: In computing a measure of the central tendency for any set of 51 numbers, which one of the following measures is well-defined but uses only very few of the numbers of the set?
a) Arithmetic mean
b) Geometric mean
c) Median
d) Mode
Answer: d

Question: The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average rises by 1/2 kg; the weight of the teacher is:
a) 40.5 kg
b) 50 kg
c) 41 kg
d) 58 kg
Answer: d

Question: For the given data, the calculation corresponding to all values of pairs (x, y) is following ∑(x–x̅)2= 36, ∑(y–y̅)2 = 25 (x–x̅)(y–y̅) = 20 , Then the Karl Pearson’s correlation coefficient is: C
a) 0.2
b) 0.5
c) 0.66
d) 0.33
Answer: c

Question: In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is
a) 6
b) 7
c) 8
d) 12
Answer: b

Question: Mean deviation of the data a, a + d, a + 2d,……., a + 2nd from the mean is equal to
a) n(n + 1) |d | /2n+1
b) n(n + 1) |d | /2n+1
c) (n + 1) |d | /2n
d) None of the options
Answer: a