CBSE Class 11 Mathematics Statistics Worksheet Set 01

Multiple Choice Questions

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. The mean deviation from the mean of the set of observations −1, 0 and 4 is
(a) 3
(b) 1
(c) −2
(d) 2
Answer : D

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. Consider the following data
36, 72, 46, 42, 60, 45, 53, 46, 51, 49
Then, the mean deviation about the median for the data is
(a) 6
(b) 8
(c) 7
(d) None of the above
Answer : C

Question. The mean deviation about the median for the data
32, 34, 36, 38, 40, 42, 44, 46, 48, 50 is
(a) 4.5
(b) 4
(c) 5.5
(d) 5
Answer : D

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

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. Mean deviation about the median for the data 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17 is
(a) 2.44
(b) 2.33
(c) 1.44
(d) 1.33
Answer : B

Question. The mean deviation about the median for the data 34, 66, 30, 38, 44, 50, 40, 60, 42, 51 is
(a) 8.7
(b) 7.7
(c) 87
(d) 77
Answer : A

Question. The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then y/x is equal to:
(a) 9/4
(b) 7/2
(c) 8/3
(d) 7/3
Answer : D

Question. The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is:
(a) 15.8
(b) 14.0
(c) 16.8
(d) 16.0
Answer : B

Question. If the median and the range of four numbers {x, y, 2x + y, x – y}, where 0 < y < x < 2y, are 10 and 28 respectively, then the mean of the numbers is :
(a) 18
(b) 10
(c) 5
(d) 14
Answer : D

Question. A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is ₹ 54 and per day mean wage of all the workers is ₹ 60, then per day mean wage of the night shift workers (in ₹) is : 
(a) 69
(b) 66
(c) 74
(d) 75
Answer : C

Question. The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :
(a) 25
(b) 30
(c) 35
(d) 40
Answer : C

Question. The average marks of boys in 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) 80
(b) 60
(c) 40
(d) 20
Answer : D

Question. In a set of 2n distinct observations, each of the observations below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then the mean of the new set of observations:
(a) increases by 1
(b) decreases by 1
(c) decreases by 2
(d) increases by 2
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. The mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be : 
(a) 41
(b) 49
(c) 40.5
(d) 42.5
Answer : A

Question. The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 - 30 and the number of observations less than 20 is 45, then the frequency of median class is
(a) 10
(b) 20
(c) 15
(d) 12
Answer : A

Question. In a class of 100 students there are 70 boys whose average marks in a sub ect 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. Let x₁, x₂ , .............. xn be n observations such that ∑x_i² = 400 and ∑x_i = 80. Then the possible value of n among the following is 
(a) 15
(b) 18
(c) 9
(d) 12
Answer : B

Question. The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal to:
(a) –5
(b) 10
(c) –20
(d) –10
Answer : C

Question. If the standard deviation of the numbers –1, 0, 1, k is √5 where k > 0, then k is equal to:
(a) 2√6
(b) 2√10/2
(c) 4√5/3
(d) √6
Answer : A

Question. If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately 
(a) 22.0
(b) 20.5
(c) 25.5
(d) 24.0
Answer : D

Question. The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is :
(a) 1
(b) 4
(c) 2
(d) 3
Answer : C

Assertion-Reasoning MCQs

Directions Each of these questions contains two statements Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of the which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) A is true, R is true; R is a correct explanation of A.
(b) A is true, R is true; R is not a correct explanation of A.
(c) A is true; R is false
(d) A is false; R is true.

Question. Assertion (A) In order to find the dispersion of values of x from mean x , we take absolute measure of dispersion.
Reason (R) Sum of the deviations from mean (x ) is zero.
Answer : A

Question. Assertion (A) The mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is 3.
Reason (R) The mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
Answer : C

Question. Assertion (A) The mean deviation about median calculated for series, where variability is very high, cannot be fully relied.
Reason (R) The median is not a representative of central tendency for the series where degree of variability is very high.
Answer : A

Question. Assertion (A) The mean deviation about the mean to find measure of dispersion has certain limitations.
Reason (R) The sum of deviations from the mean is more than the sum of deviations from median. Therefore, the mean deviation about the mean is not very scientific, where degree of variability is very high.
Answer : A

Question. Assertion (A) 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 80%.
Reason (R) Mean marks scored by the students of a class is 53. The mean marks of the girls is 55 and the mean marks of the boys is 50. The percentage of girls in the class is 64%.
Answer : C

Case Based MCQs

You are given the following grouped data.

x_i  2  5   6  8  10  12
f_i  2  8  10  7   8    5

Based on these data, answer the following questions.

Question. Mean of the grouped data is
(a) 7.0
(b) 7.5
(c) 8.0
(d) 8.5
Answer : B

Question. Mean deviation about the mean is
(a) 2.1
(b) 2.2
(c) 2.3
(d) 2.4
Answer : C

Question. The value of median is
(a) 5
(b) 6
(c) 7
(d) 8
Answer : C

Question. Mean deviation about the median is
(a) 1.9
(b) 2.0
(c) 2.2
(d) 2.3
Answer : D

Question. The difference between mean and median is
(a) 0.9
(b) 0.7
(c) 0.5
(d) 0.3
Answer : C

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 11 Mathematics Worksheet - Statistics