CBSE Class 9 Maths Statistics MCQs

Question: The mean of 13 observations is 14. If the mean of the first 7 observations is 16 and that of the last 7 observations is 12, then the 7th observation is ______.
(A) 12
(B) 14
(C) 16
(D) 18
Answer : B

Question: The mean of ten items is p and if each item is decreased by 3, then its mean will be _____ .
(A) 10p – 3
(B) 3p
(C) p – 3
(D) 10 + p
Answer : C

Question: Find the median of the data given below.
14, 6, 9, 15, 14, 9, 21, 21, 25, 21, 27, 29, 21, 8, 6, 15, 25, 14, 21, 9, 21, 25, 27, 29, 6, 14, 21, 21, 27, 25, 27, 9, 15, 14, 9
(A) 25
(B) 21
(C) 14
(D) 9
Answer : B

Question: Find the mode of the given data.
7, 4, 3, 5, 6, 3, 3, 2, 4, 3, 4, 3, 3, 4, 4, 3, 2, 2, 4, 3, 5, 4, 3, 4, 3, 4, 3, 1, 2, 3
(A) 3
(B) 4
(C) 5
(D) 2
Answer : A

Question: The following observations have been arranged in the ascending order. If the median of the data 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 is 63, then the value of x is ______.
(A) 63
(B) 62
(C) 61
(D) 60
Answer : B

Question: If the mean of 6, y, 7, 14 and x is 8. Then, the value of x + y is ______.
(A) 13
(B) 12
(C) 10
(D) 15
Answer : A

Question: If the mode of the data 4, 3, 2, 5, x, 4, 5, 1, 7, 3, 2, 1 is 4, then value of x is ______.
(A) 4
(B) 3
(C) 2
(D) 1
Answer : A

Question: If x is the mean of x₁, x₂,.....,x_n, then for a ≠ 0, the mean of ax₁, ax₂,...., ax_n, x₁/a, x₂/a,...., x_n/a is_____.

Answer : B

Question: If mean of the following data is 11. Find the value of P.

(A) 11
(B) 15
(C) 17
(D) 13
Answer : B

Question: Mean of 11 observations is 17.5. If one observation value 15 is deleted, then the mean of remaining observations is ______.
(A) 15.75
(B) 16.75
(C) 17.75
(D) 18.75
Answer : C

Question: Find the mean of two digit natural numbers which have both digits same.
(A) 55
(B) 45
(C) 65
(D) 50
Answer : A

Question: In a class test, in Mathematics, 10 students scored 75 marks, 12 students scored 60 marks, 8 students scored 40 marks and 3 students scored 30 marks. The mean of their score is (approximately) ______.
(A) 57 marks
(B) 56 marks
(C) 15 marks
(D) 54 marks
Answer : A

Question: In a class, the mean weight of 60 students is 40 kg. The mean weight of boys is 50 kg while that of the girls is 30 kg. The number of boys and girls respectively are ______.
(A) 30, 30
(B) 35, 25
(C) 25, 35
(D) 20, 40
Answer : A

Question: The mean of 11 numbers is 10. What should be added as 12th number to make the mean 14?
(A) 10
(B) 72
(C) 58
(D) 90
Answer : C

Question: If the mean of 10 observations is 20 and that of another 15 observations is 16, then the mean of 25 observations is ______.
(A) 18
(B) 18.2
(C) 17.6
(D) 17
Answer : C

Question: The mode of a set of observations is the value which
a) occurs most frequently
b) is between maximum and minimum
c) is central
d) none of the foregoing
Answer: A

Question: The arithmetic mean for the following frequency distribution is

a) 26.5
b) 43.8
c) 42.3
d) 29.5
Answer: A

Question: The sum of the squares of two consecutive even numbers is two more than two times the square of their mean. This statement is
(A) Never true
(B) Always true
(C) True when the numbers are more than 100.
(D) True when the numbers are less than or equal to 100.
Answer : B

Question: Match the following

      P       Q      R       S
(A) 3       1       2       4
(B) 3       1       4       2
(C) 1       3       2       4
(D) 1       3       4       2
Answer : B

Question: The mean of 6, y, 7, x and 14 is 8. Then
a) x + y = 13
b) 2x + 3y = 13
c) x – y = 13
d) None of these
Answer: A

Question: The mean of 994, 996, 998, 1000 and 1002 is
a) 998
b) 992
c) 1004
d) none
Answer: A

Question: State ‘T’ for true and ‘F’ for false.
(i) If the number of observations is even, then the median is mean of (n/2)th and (n/2+1)th terms.
(ii) After four vertical lines for a tally marks, if the tally marks occurs for the fifth time, then the fifth line is put vertically with previous four lines.
(iii) If the range of the data with minimum value 16, is 87, then the maximum value is 71
(iv) Mode of the data, 14, 71, 51, 91, 15, 2, 15, 51, 19, 41, 51, 15, 51 is 51.
(v) Mean of first ten natural numbers is 5.5
      (i)    (ii)    (iii)    (iv)    (v)
(A) T       F       T       T       T
(B) F       F       T       T       T
(C) T       F       F       T       T
(D) T       F       T       F       T
Answer : C

Question: Arnav scored 63 marks in English, 57 in Hindi, 82 in Mathematics, 55 in Social Science and x in Science. If the average he scored is 60, find the average of best four of the them.
(A) 63.25
(B) 65.15
(C) 64.25
(D) 60.75
Answer : C

Question: The arithmetic mean of first five natural numbers is
a) 3
b) 5
c) 4
d) 6
Answer: A

Question: If the arithmetic mean of 6, 8, 5, 7, x and 4 is 7, then x is
a) 12
b) 8
c) 6
d) 4
Answer: A

Question: Fill in the blanks.
(i) The P of class interval is called its class mark.
(ii) The Q can be calculated graphically.
(iii) The R of all bars in histogram should be equal.
(iv) Width of the class interval called S of class interval.
             P                          Q             R               S
(A) Lower value         median       width          range
(B) Mid-value             mean          length        range
(C) Mid-value             median       width          size
(D) Upper-value         mode          length        size
Answer : C

Question: The mean of 10 observation is 25. If one observation, namely 25, is deleted, the new mean is
a) 25
b) 28
c) 20
d) 22
Answer: A

Question: Mean of the set of observations is the value which
a) is a representative of whole group
b) occurs most frequently
c) divides observations into two equal parts
d) is the sum of observations
Answer: A

Question: If each entry of a data is increased by 5, then the arithmetic mean
a) increases by 5
b) none of the foregoing
c) remains the same
d) decreases by 5
Answer: A

Question: The arithmetic mean of five given numbers is 85. Their sum is
a) 425
b) 85
c) more than 425
d) between 85 and 425
Answer: A

Question: The daily earnings (in rupees) of 10 workers in a factory are 8, 16, 19, 8, 16, 19, 16, 8, 19, 19. The median wage is
a) Rs. 16.00
b) Rs. 8.00
c) Rs. 17.50
d) Rs. 19.00
Answer: A

Question: The average weight of sample of 10 apples is 52 g. Later it was found that the weighing machine had shown the weight of each apple 10 g less. The correct average weight of an apple is
a) 62 g
b) 56 g
c) 54g
d) 52 g
Answer: A

Question: In a school, there are 40 students in which boys and girls are in the ratio 3 : 1. The mean age of the boys is 20 years and the mean age of the girls is 18 years. If there is increase in girls by 5 and decrease in boys by 10, then find the new average age (approx.) when the students joining or leaving doesn’t change the average age of boys and girls respectively.
(A) 15 years
(B) 19 years
(C) 16 years
(D) Can’t say
Answer : B

Question: The owner of a plant nursery wanted to test the effectiveness of a new type of fertilizer.
He measured the heights of 5 plants, and then gave each an equal amount of fertilizer. Two weeks later, he measured the heights of the plants again. The graph below shows the height of the plants before and after the addition of fertilizer.

What was the mean growth of the plants ?
(A) 4.5 cm
(B) 5 cm
(C) 5.5 cm
(D) 6 cm
Answer : A

Question: The arithmetic mean of first ten natural numbers is
a) 5.5
b) 7.5
c) 6
d) 10
Answer: A

Question: The average of n numbers x1, x2, x3,........, xn is A. If x1 is replaced by (x + a) x1, x2 is replaced by (x + a) x2,......., then the new average is ______.
(A) (x + a) A
(B) (x-1)A+nxn/n
(C) nA+(n+1)xn/n
(D) (n+1)A+xn/n
Answer : A

Question: The difference between the maximum and the minimum observation in the data is called ______.
(A) Frequency
(B) Class interval
(C) Range
(D) Cumulative frequency
Answer : C

Question: A contractor employed 18 labourers at ₹ 12 each per day, 10 labourers at ₹ 13.50 each per day, 5 labourers at ₹ 25 each per day and 2 labourers at ₹ 42 each per day. The average wages paid is ______.
(A) ₹ 16
(B) ₹ 20
(C) ₹ 24
(D) ₹ 28
Answer : A

Question: The weight (in kg) of 5 men are 62, 65, 69, 66 and 61. The median is
a) 65 kg
b) 45 kg
c) 55 kg
d) 66 kg
Answer: A

Question: Class mark and class size of the class interval are 25 and 10 respectively then the class interval is
(a) 20 – 30
(b) 30 – 40
(c) 40 – 50
(d) 50 – 60

Question: Class mark of the 1st class interval is 5 and there are five classes. If the class size is 10 then the last class interval is
(a) 20 – 30
(b) 30 – 40
(c) 40 – 50
(d) 50 – 60

Question: The median of the following data is

(a) 10
(b) 15
(c) 25
(d) 30

Question: The mode in the above frequency distribution table is
(a) 10
(b) 15
(c) 25
(d) 30

Question: The mean of the following data is 

(a) 15
(b) 16
(c) 17
(d) none of these

Question: The median of first ten prime numbers is
(a) 11
(b) 12
(c) 13
(d) none of these.

Question: The mean of first ten multiples of 5 is
(a) 45
(b) 55
(c) 65
(d) none of these.

Question: The mean of first ten multiples of 2 is
(a) 11
(b) 12
(c) 13
(d) none of these.

Question: The median of first ten multiples of 3 is
(a) 15
(b) 16
(c) 16.5
(d) none of these.

Question: The median of the following data is

(a) 20
(b) 30
(c) 40
(d) none of these

Question: The median of the following data is 25 72 28 65 29 60 30 54 32 53 33 52 35 51 42 48 45 47 46 33
(a) 45
(b) 45.5
(c) 46
(d) none of these

Question: Calculate the median income from the following data: 

(a) 20
(b) 30
(c) 40
(d) none of these

Question. Class mark of class 150 – 160 is
(a) 150
(b) 160
(c) 155
(d) none of these.

Question. Average of numbers: 10, 8, 9, 7, 8 is
(a) 8.4
(b) 7.4
(c) 4.8
(d) 8.2.

Question. Mean of first 10 natural numbers is
(a) 6.5
(b) 5.5
(c) 7.5
(d) 8.5.

Question. The heights (in cm) of 9 students of a class are as follows: 
155, 160, 145, 149, 150, 147, 152, 144, 148 Find the median of this data.
(a) 150
(b) 147
(c) 149
(d) 148

Question. The points scored by a Kabaddi team in a series of matches are as follows 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28 Find the median of the points scored by the team.
(a) 12
(b) 15
(c) 24
(d) 28

Question. Find the mode of the following marks (out of 10) obtained by 20 students: 4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9
(a) 4
(b) 7
(c) 10
(d) 9

Question. 5 people were asked about the time in a week they spend in doing social work in their community. They said 10, 7, 13, 20 and 15 hours, respectively. Find the mean (or average) time in a week devoted by them for social work.
(a) 12
(b) 13
(c) 14
(d) none of these.

Question. The width of each of five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class limit of the lowest class is 10. The upper class limit of the highest class is:
(a) 35
(b) 15
(c) 25
(d) 40

Question. Let m be the midpoint and ‘l’ the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is
(a) 2m + l
(b) 2m – l
(c) m - l
(d) m – 2l

Question. The class marks of a frequency distribution are given as follows: 15, 20,25, …… The class corresponding to the class mark 20 is
(a) 12.5 – 17.5
(b) 17.5 – 22.5
(c) 22.5 – 27.5
(d) 27.5 – 32.5

Question. In the class intervals 10 – 20, 20 – 30, the cumber 20 is included in.
(a) 10 – 20
(b) 20 – 30
(c) both the interval
(d) none of these intervals

Question. The mean of 5 numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is
(a) 28
(b) 30
(c) 35
(d) 38.

Question. Class mark of class 150 – 160 is
(a) 150
(b) 160
(c) 155
(d) none of these.

Question. A grouped frequency distribution table with class intervals of equal sizes using 250 – 270 as one of the class interval is constructed for the following data:
268, 220, 368, 258, 242, 310, 272, 342, 310, 290, 300, 320, 319, 304, 402, 318, 406, 292, 354, 278, 210, 240, 330, 316, 406, 215, 258, 236 The frequency of the class 310 – 330 is
(a) 4
(b) 5
(c) 6
(d) 7.

Question. To draw a histogram to represent the following frequency distribution: the adjusted frequency for the class interval 25 – 45 is

(a) 6
(b) 5
(c) 2
(d) 3

Question. If each observation of the data is increased by 5 then their mean
(a) remains the same
(b) becomes 5 times the original mean
(c) is decreased by 5
(d) is increased by 5.

Question. There are 50 numbers. Each number s subtracted from 53 and the mean of the number so obtained is found to be 3.5. The mean of the given number is
(a) 46.5
(b) 49.5
(c) 53.5
(d) 56.5.

Question. The mean of 25 observations is 36. Out of these observations if the men of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is
(a) 23
(b) 36
(c) 38
(d) 40.

Question. The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is
(a) 45
(b) 49.5
(c) 54
(d) 56.

Question. For drawing a frequency polygon of a continuous frequency distribution, we plot the points whose ordinates are the frequency of the respective classes and abscissa re respectively
(a) upper limits of the classes
(b) lower limits of the classes
(c) class marks of the classes
(d) upper limits of preceding classes.

Collection and tabulation of date

1. The word data means information in the form of numerical figures or a set of given information

2. Data obtained in the original form is called a raw data.

3. Arranging the numerical figures of a data in ascending or descending order is called an array.

4. Arranging the data in a systematic tabular form is called tabulation or presentation of the data.

5. Each numerical figure in a data is called an observation.

6. The number of times a particular observation occurs is called its frequency.

7. The difference between the highest and lowest values of the observations in a given data is called its range.

8. Mean  = sumof all observations/number of observations

9. A table showing the frequencies of various observations of data is called a frequency distribution or simply a frequency table.

10. When the number of observations is large, we make used of tally marks to find the frequencies.

11. Tallies are usually marked in a bunch of five for the case of counting.

12. When the list of observations is long, the data is usually organised into groups called class intervals and the data so obtained is called a grouped data.

13. The lower value of a class interval is called its lower limit and the upper value is called its upper limit.

14. The difference between the upper and lower class limits is called the width or the size of the class interval.

15. The mid-value of a class interval is called its class mark.

Graphical representation

1. A histogram is a pictorial representation of the grouped data in which class intervals are taken along the horizontal axis and class frequencies along the vertical axis and for each class a rectangle is constructed with base as the class interval and height determined from the class frequency.

2. In a bar graph, bars of uniform width are drawn with various heights. The height of a column represents the frequency of the corresponding observation.

3. In a pie-chart the values of different are represented by the sectors of a circle. The total angle of 360° at the centre of a circle is divided according to the values of the components.
Central angle for a component = value of the component/total value x 360°

Mean, mode and median

1. Mean in statistics is same as the average in arithmetic.
For a raw data 
Mean = sumof all observations/number of observations
Mean of n numbers = sumof the numbers/number of addends

2. Mean of tabulated data : Let the frequencies of n observations x₁, x₂, x₃.....xn be f₁, f₂, f₃....fn respectively. Then, we define 

where ∑ (sigma) is the Greek letter for summation.

3. Mean of grouped data : In a class interval, we take x as the value of the class mark and use the formula
mean = ∑(f.x)/∑ f

4. Mode : The observation which occurs for maximum number of times is called the mode of the given data. In a tabulated data, the observation with maximum frequency is the mode.

5. Median : After arranging data in ascending or descending order of magnitudes the value of the middle term is called the median of the data.
(i) When the number of observations is odd, then there will be only one mid term and this term is the median.
(ii) When the number of observations is even, then there will be two middle terms. The average of these two middle terms will be the median of the data.

Question. The mean of 10 observation is 25. If one observation, namely 25, is deleted, the new mean is
(A) 25
(B) 20
(C) 28
(D) 22

Answer: A

Question. Mean of the set of observations is the value which
(A) occurs most frequently
(B) divides observations into two equal parts
(C) is a representative of whole group
(D) is the sum of observations

Answer: C

Question. If each entry of a data is increased by 5, then the arithmetic mean
(A) remains the same
(B) increases by 5
(C) decreases by 5
(D) none of the foregoing

Answer: B

Question. The arithmetic mean of five given numbers is 85. Their sum is
(A) 425
(B) 85
(C) between 85 and 425
(D) more than 425

Answer: A

Question. The daily earnings (in rupees) of 10 workers in a factory are 8, 16, 19, 8, 16, 19, 16, 8, 19, 19. The median wage is
(A) Rs. 17.50
(B) Rs. 8.00
(C) Rs. 19.00
(D) Rs. 16.00

Answer: D

Question. The average weight of sample of 10 apples is 52 g. Later it was found that the weighing machine had shown the weight of each apple 10 g less. The correct average weight of an apple is
(A) 62 g
(B) 54g
(C) 56 g
(D) 52 g

Answer: A

Question. The mean of 6, y, 7, x and 14 is 8. Then
(A) x + y = 13
(B) x – y = 13
(C) 2x + 3y = 13
(D) x² + y² = 15

Answer: A

Question. The mean of 994, 996, 998, 1000 and 1002 is
(A) 992
(B) 1004
(C) 998
(D) none

Answer: C

Question. The mode of a set of observations is the value which
(A) occurs most frequently
(B) is central
(C) is between maximum and minimum
(D) none of the foregoing

Answer: A

Question. The arithmetic mean for the following frequency distribution is 

(A) 26.5
(B) 42.3
(C) 43.8
(D) 29.5

Answer: A

Question. The arithmetic mean of first five natural numbers is
(A) 3
(B) 4
(C) 5
(D) 6

Answer: A

Question. If the arithmetic mean of 6, 8, 5, 7, x and 4 is 7, then x is
(A) 12
(B) 6
(C) 8
(D) 4

Answer: A

Question. The arithmetic mean of first ten natural numbers is
(A) 5.5
(B) 6
(C) 7.5
(D) 10

Answer: A

Question. The weight (in kg) of 5 men are 62, 65, 69, 66 and 61. The median is
(A) 45 kg
(B) 66 kg
(C) 65 kg
(D) 55 kg

Answer: C

Question. If in a data, 10 numbers arranged in increasing order. If the 7th entry is increased by 4, then the median increases by
(A) zero
(B) 4
(C) 6
(D) 5

Answer: A

Question. The mean of x, x + 3, x + 6, x + 9 and x + 12 is
(A) x + 6
(B) x + 3
(C) x + 9
(D) x + 12

Answer: A

Question. 20 years ago, when my parents got married, their average age was 23 years, now the average age of my family, consisting of myself and my parents only is 35 years. My present age is
(A) 34 years
(B) 42 years
(C) 24 years
(D) 16 years

Answer: D

Question. The daily sale of kerosene (in liters) in a ration shop for six days is as follows:
75, 120, 12, 50, 70.5 and 140.5. The average daily sale is
(A) 150
(B) 10
(C) 142
(D) 78

Answer: D

Question. The mean of five numbers is 27. If one of the numbers is excluded the mean gets reduced by 2. The excluded numbers is
(A) 35
(B) 27
(C) 25
(D) 40

Answer: A

Question. The median of the following data: 46, 64, 87, 41, 58, 77, 35, 90, 55, 33, 92 is
(A) 87
(B) 77
(C) 58
(D) 60.2

Answer: C

Question. A car runs for t₁ hours at v₁ km/h, t₂ hours at v₂ km/h. What is the average speed of the car for the entire journey? 

Answer: A

Question. A car runs x km at an average speed of v₁ km/h, and y km at an average speed of v₂ km/h. What is the average speed of the train for the entire journey?
(A) x+y/v₁+v₂
(B) v₁v₂(x+y)/xv₂+yv₁
(C) x₁v₁+x₂v₂/v₁+v₂
(D) None of these

Answer: B

Question. Of three numbers, the first is twice the second and thrice the third, the average of all the three numbers is 88, then the smallest number as
(A) 72
(B) 46
(C) 48
(D) 52

Answer: C

Question. The average age of m boys is ‘b’ years and ‘n’ girls is ‘c’ years. Find the average age of all together 
(A) mb-nc/m - n
(B) mb-nc/m + n
(C) mb+nc/m + n
(D) mb+nc/m-n

Answer: C

Question. 

Answer: B

Question. Rohit goes from a place to another and returns by the same route. He pedals his way uniformly with speed u while going amnd with speed v while returning. The average speed of his journey is
(A) 1/1/2(1/u+1/v)
(B) 1/2(1/u-1/v)
(C) 1/1/2(u-v)
(D) u+v/2

Answer: A

Question. In class of 100 students the mean marks obtained in a subject is 30 and in another class of 50 students the mean marks obtained in the same subject is 60. The mean marks obtained by the students of two classes taken together is
(A) 60
(B) 55
(C) 40
(D) 35

Answer: C

Question. A man lands Rs. 1200 in four sums. If he gets 5% for Rs. 300, 6% for Rs. 350 and 6.5% for Rs. 400.
What average interest is 6.5%?
(A) 31%
(B) 6%
(C) 31/3%
(D) 33/3%

Answer: D

Question. The average noon temperature for monday, tuesday and wednesday was 53° and for tuesday, wednesday and thursday it was 56°. If the noon temperature on thursday was 60°. Find the noon temperature on monday
(A) 51°
(B) 53°
(C) 56°
(D) 57°

Answer: A

Question. One third of a centain journey was covered at a rate of 25 km/h one-fourth at the rate of 30 km/h and the rest at the rate of 50 km/h. Find the average speed per hour for the whole journey? 

Answer: B