NCERT Exemplar Solutions
Class 7 - MathematicsUnit 3: Data Handling
Class 7 - Mathematics
Multiple Choice Questions
Question. 1
Let x, y, z be three observations. The mean of these observations is
\(\dfrac{x \times y \times z}{3}\)
\(\dfrac{x+y+z}{3}\)
\(\dfrac{x-y-z}{3}\)
\(\dfrac{x \times y + z}{3}\)
Open
Question. 2
The number of trees in different parks of a city are 33, 38, 48, 33, 34, 34, 33 and 24. The mode of this data is
24
34
33
48
Open
Question. 3
Which measures of central tendency get affected if the extreme observations on both the ends of a data arranged in descending order are removed?
Mean and mode
Mean and Median
Mode and Median
Mean, Median and Mode
Open
Question. 4
The range of the data: 21, 6, 17, 18, 12, 8, 4, 13 is
17
12
8
15
Open
Question. 5
The median of the data: 3, 4, 5, 6, 7, 3, 4 is
5
3
4
6
Open
Question. 6
Out of 5 brands of chocolates in a shop, a boy has to purchase the brand which is most liked by children. What measure of central tendency would be most appropriate if the data is provided to him?
Mean
Mode
Median
Any of the three
Open
Question. 7
There are 2 aces in each of the given set of cards placed face down. From which set are you certain to pick the two aces in the first go?

Open
Question. 8
In the previous question, what is the probability of picking up an ace from set (d)?
\(\dfrac{1}{6}\)
\(\dfrac{2}{6}\)
\(\dfrac{3}{6}\)
\(\dfrac{4}{6}\)
Open
Question. 9
The difference between the highest and the lowest observations in a data is its
frequency
width
range
mode
Open
Question. 10
In a school, only 2 out of 5 students can participate in a quiz. What is the chance that a student picked at random makes it to the competition?
20%
40%
50%
30%
Open
Question. 11
Some integers are marked on a board. What is the range of these integers?

31
37
20
3
Open
Question. 12
On tossing a coin, the outcome is
only head
only tail
neither head nor tail
either head or tail
Open
Question. 13
The mean of three numbers is 40. All the three numbers are different natural numbers. If lowest is 19, what could be highest possible number of remaining two numbers?
81
40
100
71
Open
Question. 14
Khilona earned scores of 97, 73 and 88 respectively in her first three examinations. If she scored 80 in the fourth examination, then her average score will be
increased by 1
increased by 1.5
decreased by 1
decreased by 1.5
Open
Question. 15
Which measure of central tendency best represents the data of the most popular politician after a debate?
Mean
Median
Mode
Any of the above
Open
Question. 16
Which of the following has the same mean, median and mode?
(a) 6, 2, 5, 4, 3, 4, 1
(b) 4, 2, 2, 1, 3, 2, 3
(c) 2, 3, 7, 3, 8, 3, 2
(d) 4, 3, 4, 3, 4, 6, 4
Open
Fill in the Blanks
Question. 17
The difference between the highest and the lowest observations of a data is called ________.
Answer:
The difference between the highest and the lowest observations of a data is called Range.
Open
Question. 18
The mean of a data is defined as ________.
Answer:
The mean of a data is defined as \(\dfrac{\text{Sum of all observations}}{\text{Number of observations}}\).
Open
Question. 19
In a set of observations, the observation that occurs the most often is called ________.
Answer:
In a set of observations, the observation that occurs the most often is called Mode.
Open
Question. 20
In a given data, arranged in ascending or descending order, the middle most observation is called ________.
Answer:
In a given data, arranged in ascending or descending order, the middle most observation is called Median.
Open
Question. 21
Mean, Median, Mode are the measures of ________.
Answer:
Mean, Median, Mode are the measures of Central tendency.
Open
Question. 22
The probability of an event which is certain to happen is ________.
Answer:
The probability of an event which is certain to happen is 1.
Open
Question. 23
The probability of an event which is impossible to happen is ________.
Answer:
The probability of an event which is impossible to happen is 0.
Open
Question. 24
When a die is thrown, the probability of getting a number less than 7 is ________.
Answer:
When a die is thrown, the probability of getting a number less than 7 is 1.
Open
Question. 25
In throwing a die the number of possible outcomes is ________.
Answer:
In throwing a die the number of possible outcomes is 6.
Open
Question. 26
________ can be used to compare two collections of data.
Answer:
A double bar graph can be used to compare two collections of data.
Open
Question. 27
The representation of data with bars of uniform width is called ________.
Answer:
The representation of data with bars of uniform width is called Bar graph.
Open
Question. 28
If the arithmetic mean of 8, 4, x, 6, 2, 7 is 5, then the value of x is ________.
Answer:
If the arithmetic mean of 8, 4, x, 6, 2, 7 is 5, then the value of x is 3.
Open
Question. 29
The median of any data lies between the ________ and ________ observations.
Answer:
The median of any data lies between the Minimum and Maximum observations.
Open
Question. 30
Median is one of the observations in the data if number of observations is ________.
Answer:
Median is one of the observations in the data if number of observations is Odd.
Open
Question. 31
Rohit collected the data regarding weights of students of his class and prepared the following table:
| Weight (in kg) | 44–47 | 48–51 | 52–55 | 56–60 |
|---|---|---|---|---|
| Number of Students | 3 | 5 | 25 | 7 |
A student is to be selected randomly from his class for some competition. The probability of selection of the student is highest whose weight is in the interval ________.
Answer:
The probability of selection of the student is highest whose weight is in the interval 52–55.
Open
True or False Questions
Question. 32
If a die is thrown, the probability of getting a number greater than 6 is 1.
Answer:
Open
Question. 33
When a coin is tossed, there are 2 possible outcomes.
Answer:
Open
Question. 34
If the extreme observations on both the ends of a data arranged in ascending order are removed, the median gets affected.
Answer:
Open
Question. 35
The measures of central tendency may not lie between the maximum and minimum values of data.
Answer:
Open
Question. 36
It is impossible to get a sum of 14 of the numbers on both dice when a pair of dice is thrown together.
Answer:
Open
Question. 37
The probability of the spinning arrow stopping in the shaded region (Fig. 3.4) is \(\dfrac{1}{2}\).

Answer:
Open
Question. 38
A coin is tossed 15 times and the outcomes are recorded as follows: H T T H T H H H T T H T H T T. The chance of occurrence of a head is 50 per cent.
Answer:
Open
Question. 39
Mean, Median and Mode may be the same for some data.
Answer:
Open
Question. 40
The probability of getting an ace out of a deck of cards is greater than 1.
Answer:
Open
Question. 41
Mean of the data is always from the given data.
Answer:
Open
Question. 42
Median of the data may or may not be from the given data.
Answer:
Open
Question. 43
Mode of the data is always from the given data.
Answer:
Open
Question. 44
Mean of the observations can be lesser than each of the observations.
Answer:
Open
Question. 47
The data 12, 13, 14, 15, 16 has every observation as mode.
Answer:
Open
Question. 48
The range of the data 2, −5, 4, 3, 7, 6 would change if 2 was subtracted from each value in the data.
Answer:
Open
Question. 49
The range of the data 3, 7, 1, −2, 2, 6, −3, −5 would change if 8 was added to each value in the data.
Answer:
Open
Problems and Solutions
Question. 50
Calculate the Mean, Median and Mode of the following data: 5, 10, 10, 12, 13.
Are these three equal?
Answer:
Mean = 10, Median = 10, Mode = 10. Yes, all three are equal.
Open
Question. 51
Find the mean of the first ten even natural numbers.
Answer:
11
Open
Question. 52
A data constitutes of heights (in cm) of 50 children. What do you understand by mode for the data?
Answer:
Mode is the observation that occurs most frequently in a set of observations.
Open
Question. 53
A car seller collects the following data of cars sold in his shop:
| Colour of Car | Number of Cars Sold |
|---|---|
| Red | 15 |
| Black | 20 |
| White | 17 |
| Silver | 12 |
| Others | 9 |
(a) Which colour of the car is most liked?
(b) Which measure of central tendency was used in (a)?
Answer:
(a) Black
(b) Mode
Open
Question. 54
The marks in a subject for 12 students are as follows: 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29.
For the given data, find the
(a) Range (b) Mean (c) Median (d) Mode
Answer:
(a) 25
(b) 30.41
(c) 33
(d) 35
Open
Question. 55
The following are weights (in kg) of 12 people: 70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78, 60.
(a) Find the mean of the weights of the people.
(b) How many people weigh above the mean weight?
(c) Find the range of the given data.
Answer:
(a) 65.6
(b) 4
(c) 30
Open
Question. 56
Following cards are put facing down: A, E, I, O, U. What is the chance of drawing out
(a) a vowel
(b) A or I
(c) a card marked U
(d) a consonant
Answer:
(a) 1
(b) 2/5
(c) 1/5
(d) 0
Open
Question. 57
For the given data calculate the mean of its median and mode: 6, 2, 5, 4, 3, 4, 4, 2, 3.
Answer:
4
Open
Question. 58
Find the median of the given data if the mean is 4.5: 5, 7, 7, 8, x, 5, 4, 3, 1, 2.
Answer:
4.5
Open
Question. 59
What is the probability of the sun setting tomorrow?
Answer:
One
Open
Question. 60
When a spinner with three colours (Fig. 3.5) is rotated, which colour has more chance to show up with arrow than the others?

Answer:
Blue
Open
Question. 61
What is the probability that a student chosen at random out of 3 girls and 4 boys is a boy?
Answer:
4/7
Open
Question. 62
The letters written on paper slips of the word MEDIAN are put in a bag. If one slip is drawn randomly, what is the probability that it bears the letter D?
Answer:
1/6
Open
Question. 63
Classify the following events as certain to happen, impossible to happen, may or may not happen:
(a) Getting a number less than 1 on throwing a die.
(b) Getting head when a coin is tossed.
(c) A team winning the match.
(d) Christmas will be on 25 December.
(e) Today moon will not revolve around the earth.
(f) A ball thrown up in the air will fall down after some time.
Answer:
(a) Impossible to happen
(b) May or may not happen
(c) May or may not happen
(d) Certain to happen
(e) Impossible to happen
(f) Certain to happen
Open
Question. 64
A die was thrown 15 times and the outcomes recorded were 5, 3, 4, 1, 2, 6, 4, 2, 2, 3, 1, 5, 6, 1, 2. Find the mean, median and mode of the data.
Answer:
Mean = 3.13, Median = 3, Mode = 2
Open
Question. 66
Find the median of first nine even natural numbers.
Answer:
10
Open
Question. 67
The mean of three numbers is 10. The mean of other four numbers is 12. Find the mean of all the numbers.
Answer:
11.14
Open
Question. 68
Find the mode of the given data: 10, 8, 4, 7, 8, 11, 15, 8, 4, 2, 3, 6, 8.
Answer:
8
Open
Question. 69
Heights of 15 boys (in cm): 128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.
Find (a) The height of the tallest boy.
(b) The height of the shortest boy.
(c) The range of the given data.
(d) The median height of the boys.
Answer:
(a) 154 cm
(b) 128 cm
(c) 26 cm
(d) 142 cm
Open
Question. 70
Observe the data and answer:
16, 15, 16, 16, 8, 15, 17
(a) Which data value can be put in the data so that the mode remains the same?
(b) At least how many and which value(s) must be put in to change the mode to 15?
(c) What is the least number of data values that must be put in to change the mode to 17? Name them.
Answer:
(a) 8 or 17 or 16 (except 15)
(b) Two times 15
(c) Three times 17
Open
Question. 71
Ages (in years) of 6 children of two groups are recorded as below:
| Group A | Group B |
|---|---|
| 7 | 7 |
| 7 | 9 |
| 9 | 11 |
| 8 | 12 |
| 10 | 12 |
| 10 | 12 |
(a) Find the mode and range for each group.
(b) Find the range and mode if the two groups are combined together.
Answer:
(a) Group A: Mode = 7 and 10, Range = 3.
Group B: Mode = 12, Range = 5.
(b) Combined: Range = 5, Mode = 7 and 12.
Open
Question. 72
Observe the given bar graph carefully and answer the questions that follow.

(a) What information does the bar graph depict?
(b) How many motor bikes were produced in the first three months?
(c) Calculate the increase in production in May over the production in January.
(d) In which month the production was minimum and what was it?
(e) Calculate the average (mean) production of bikes in 6 months.
Answer:
(a) Production of motor bikes by XYZ Automobiles Ltd. during January to June.
(b) 2100
(c) 300
(d) June, 500
(e) 767 bikes (nearest whole number)
Open
Question. 73
The bar graph given below shows the marks of students of a class in a particular subject:

(a) If 40 is the pass mark, then how many students have failed?
(b) How many students got marks from 50 to 69?
(c) How many students scored 90 marks and above?
(d) If students who scored marks above 80 are given merits then how many merit holders are there?
(e) What is the strength of the class?
Answer:
(a) 4
(b) 18
(c) 4
(d) 10
(e) 42
Open
Question. 74
Study the bar graph given below and answer the questions that follow.

(a) What information does the above bar graph represent?
(b) In which year was production the least?
(c) After which year was the maximum rise in the production?
(d) Find the average production of rice during the 5 years.
(e) Find difference of rice production between years 2006 and 2008.
Answer:
(a) The production of rice (in million tonnes) by a country during the years 2005 to 2009
(b) 2006
(c) 2006
(d) 54 million tonnes
(e) 10 million tonnes
Open
Question. 75
Study the bar graph given below and answer the questions that follow:

(a) What information is depicted from the bar graph?
(b) In which subject is the student very good?
(c) Calculate the average marks of the student.
(d) If 75 and above marks denote a distinction, then name the subjects in which the student got distinction.
(e) Calculate the percentage of marks the student got out of 500.
Answer:
(a) Marks obtained by a student in different subjects
(b) Maths
(c) 68.2
(d) Hindi, Maths
(e) 68.2%
Open
Question. 76
The bar graph given below represents the circulation of newspapers (dailies) in a town in six languages (figures approx. to hundreds).

(a) Find the total number of newspapers read in Hindi, Punjabi, Urdu, Marathi and Tamil.
(b) Find the excess number of newspapers read in Hindi than those in English.
(c) Name the language in which the least number of newspapers are read.
(d) Write the total circulation of newspapers in the town.
Answer:
(a) 1800
(b) 300
(c) Tamil
(d) 2300
Open
Question. 77
Study the double bar graphs given below and answer the following questions:

(a) Which sport is liked the most by Class VIII students?
(b) How many students of Class VII like Hockey and Tennis in all?
(c) How many students are there in Class VII?
(d) For which sport is the number of students of Class VII less than that of Class VIII?
(e) For how many sports students of Class VIII are less than Class VII?
(f) Find the ratio of students who like Badminton in Class VII to students who like Tennis in Class VIII.
Answer:
(a) Cricket
(b) 17
(c) 65
(d) Cricket
(e) 4 sports (Hockey, Football, Tennis, Badminton)
(f) 14:7 or 2:1
Open
Question. 78
Study the double bar graph shown below and answer the questions that follow:

(a) What information is represented by the above double bar graph?
(b) In which month sales of Brand A decreased as compared to the previous month?
(c) What is the difference in sales of both the Brands for the month of June?
(d) Find the average sales of Brand B for the six months.
(e) List all months for which the sales of Brand B was less than that of Brand A.
(f) Find the ratio of sales of Brand A as compared to Brand B for the month of January.
Answer:
(a) Comparison of sales of Brand A and Brand B during the month of January to June
(b) March
(c) 3 Lakh
(d) 41.8 Lakh
(e) April, June
(f) 31:36
Open
Question. 79
Study the double bar graph given below and answer the questions that follow:

(a) What information is compared in the above given double bar graph?
(b) Calculate the ratio of minimum temperatures in the year 2008 to the year 2009 for the month of November.
(c) For how many months was the minimum temperature in the year 2008 greater than that of year 2009? Name those months.
(d) Find the average minimum temperature for the year 2008 for the four months.
(e) In which month is the variation in the two temperatures maximum?
Answer:
(a) Comparison of minimum temperature during Nov–Feb for 2008 and 2009
(b) 18:15 or 6:5
(c) Two: February and November
(d) 11.25
(e) February
Open
Question. 80
The following table shows the average intake of nutrients in calories by rural and urban groups in a particular year. Using a suitable scale for the given data, draw a double bar graph to compare the data.
| Foodstuff | Rural | Urban |
|---|---|---|
| Pulses | 35 | 49 |
| Leafy vegetables | 14 | 21 |
| Other vegetables | 51 | 89 |
| Fruits | 35 | 66 |
| Milk | 70 | 250 |
| Fish and flesh foods | 10 | 22 |
| Fats and Oils | 9 | 35 |
| Sugar/Jaggery | 19 | 31 |
Answer:
Give the double bar graph here
Open
Question. 81
Study the double bar graph and answer the questions that follow:

(a) What information does the double bar graph represent?
(b) Find the total number of boys in all sections of Class VII.
(c) In which sections, the number of girls is greater than the number of boys?
(d) In which section, the number of boys is the maximum?
(e) In which section, the number of girls is the least?
Answer:
(a) Number of students (boys and girls) in different sections of Class VII
(b) 110 boys
(c) Sections VII A and VII D
(d) VII B
(e) VII C
Open
Question. 82
In a public library, the following observations were recorded by the librarian in a particular week:
| Days | Mon | Tues | Wed | Thurs | Fri | Sat |
|---|---|---|---|---|---|---|
| Newspaper Readers | 400 | 600 | 350 | 550 | 500 | 350 |
| Magazine Readers | 150 | 100 | 200 | 300 | 250 | 200 |
(a) Draw a double bar graph choosing an appropriate scale.
(b) On which day, the number of readers in the library was maximum?
(c) What is the mean number of magazine readers?
Answer:
(a) Give the double bar graph here
(b) Thursday
(c) 200
Open
Question. 83
Observe the following data:
| Class | Total Students | Number of Students Present on that Day |
|---|---|---|
| VI | 90 | 81 |
| VII | 82 | 76 |
| VIII | 95 | 91 |
| IX | 70 | 65 |
| X | 63 | 62 |
(a) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
(b) Which class has the maximum number of students?
(c) In which class, the difference of total students and number of students present is minimum?
(d) Find the ratio of number of students present to the total number of students of Class IX.
(e) What per cent of Class VI students were absent?
Answer:
(a) Give the double bar graph here
(b) VIII
(c) X
(d) 13:14
(e) 10%
Open
Question. 84
Observe the given data:
| Days of the Week | Mon | Tues | Wed | Thurs | Fri | Sat |
|---|---|---|---|---|---|---|
| Number of Mobile Phone Sets Sold | 50 | 45 | 30 | 55 | 27 | 60 |
(a) Draw a bar graph to represent the above given information.
(b) On which day of the week was the sales maximum?
(c) Find the total sales during the week.
(d) Find the ratio of the minimum sale to the maximum sale.
(e) Calculate the average sale during the week.
(f) On how many days of the week was the sale above the average sales?
Answer:
(a) Give the bar graph here
(b) Saturday
(c) 267
(d) 9:20
(e) 44.5
(f) 4 days (Mon, Tue, Thu, Sat)
Open
Question. 85
Below is a list of 10 tallest buildings in India...
(a) Find the height of each storey of the three tallest buildings and write them.
(b) The average height of one storey for the buildings given in (a).
(c) Which city in this list has the largest percentage of skyscrapers?
(d) What is the range of data?
(e) Find the median of the data.
(f) Draw a bar graph for given data.
Answer:
(a) Heights per storey: MVRDC (4.45), Oberoi Woods (4.25), RNA Mirage (4.25), Planet (3.5), UB Tower (9.2), Ashok (3.9), Imperial I/II (4.15).
(b) 4.45
(c) Mumbai, 81.6%
(d) 93 m
(e) 192.5
(f) Draw bar graph
Open
Question. 86
The marks out of 100 obtained by Kunal and Soni...
Answer:
(a) Draw bar graph
(b) 84%
(c) 81.6%
(d) 34:35
(e) Three subjects (Eng, Hindi, S.Sc.)
(f) Soni, 11 marks
(g) English and Science, 14 marks
Open
Question. 87
The students of Class VII have to choose one club...
Answer:
(a) Draw double bar graph
(b) 210
(c) Electronics
(d) Yoga
(e) Yoga, Dramatics
(f) Fine Arts
Open
Question. 88
The data given below shows the production of motor bikes...
Answer:
(a) Draw double bar graph
(b) 2007
(c) 4420
(d) May
(e) August
(f) February
Open
Question. 89
The table below compares the population...
Answer:
(a) Draw double bar graph
(b) Town D
(c) Town A
Open
Question. 90
The table below gives the data of tourists visiting 5 hill stations...
Answer:
(a) Draw double bar graph
(b) Mussoorie
(c) Manali
(d) Manali, Nainital, Mussoorie, Kullu
Open
Question. 91
The table below gives the flavours of ice cream liked by children...
Answer:
(a) Draw double bar graph
(b) Butterscotch
(c) 46
(d) 21
(e) 5:6