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Important Questions Class 7 Mathematics Chapter 3 – Data Handling
Mathematics is an important subject taught in school. This subject has great importance in our daily life because the main aim of Mathematics is to solve reallife problems. The third chapter of Class 7 Mathematics deals with data handling.
Students have learnt data handling in Class 6. But in this chapter, they will learn more about it. They will study how to do mean, median and mode of the collected data. They will learn more about data collection and organisation and the basics of probability. This chapter is very important, and students must practice questions as much as possible.
Extramarks is a leading company that provides all the study materials related to CBSE and NCERT. Our experts have made the Important Questions Class 7 Mathematics Chapter 3 to help students practise. They have collected these questions from several sources, such as the CBSE sample papers, CBSE past years’ question papers, NCERT exemplars and important reference books. They have solved the questions, and experienced professionals have further checked the answers.
Extramarks provide all the study materials according to the student’s needs. You can download these study materials after registering on our official website. We provide CBSE syllabus, CBSE past years’ question papers, CBSE sample papers, CBSE extra questions, CBSE revision notes, NCERT books, NCERT exemplars, NCERT important questions, NCERT solutions, vital formulas and many more.
Important Questions Class 7 Mathematics Chapter 3 – With Solutions
Extramarks is a wellknown company that provides school students with a wide range of study materials, and our subject matter experts have made this question series so students can practise sums regularly. They have collected the questions from several sources, such as the textbook exercise, CBSE past years’ question papers, CBSE sample papers, important reference books and NCERT exemplars. They have also solved the questions in the Important Questions Class 7 Mathematics Chapter 3. Experienced professionals have further checked the answers to ensure the best quality of the content. Thus, this question series will help students to score better in exams. The important questions are
Important question class 7 chapter 3 – Data handling.
Question 1. Find the range of height of any of the ten students of a class.
Answer 1:
Let us assume that the height in cm of 10 students in a class.
= 130, 132, 135, 142, 137, 139, 140, 143, 145 and 148
By observing the abovementioned given values, the highest value is found to be= 148 cm.
By observing the abovementioned given values, the lowest value is found to be= 130 cm.
Then,
Range of Heights is equal to be = Highest value – The lowest value
= 148 – 130
= 18 cm
Question 2. Determine the Mean of the first five whole numbers.
Answer 2:
The first five Whole numbers present are 0, 1, 2, 3, and 4.
Mean is equal to = (Sum of first five whole numbers) divided by (Total Number of whole numbers)
Then,
The Sum of five whole numbers is = 0 + 1 + 2 + 3 +4
= 10
The total number of whole numbers present is = 5
Mean = (10/5)
= 2
Hence, the final Mean of the first five whole numbers is two.
Question 3. A cricketer scores the following below runs in his eight innings: 58, 46, 76, 40, 35, 45, 0 and 100. Determine the mean score.
Answer 3:
Mean score is equal to = (Total runs scored by the cricketer in all innings) divided by (Total Number of innings
Played by the cricketer)
Total runs that is scored by the cricketer in all of his innings = 58 + 76 + + 45 + 0 + 100 +40 + 35 + 46
= 400
The total number of innings is = 8
Then,
Mean is = (400/8)
= 50
Hence, the Mean score of the cricketer is 50.
Question 4. The marks out of 100 obtained by the group of students in the science test in their class are 85, 76,
90, 56, 95, 85, 39, 48, 81 and 75.
Now Find the:
(a) Highest and lowest marks obtained by the students.
(b) Range of the marks obtained.
(c) Mean marks obtained by the student’s group.
Answer 4:
Firstly, we have to arrange the marks obtained by the group of students in the science test in an ascending order, which is
= 39, 48, 56, 85, 85, 90, 95, 75, 76, 81
(a) The highest mark obtained by the student on the test is= 95
The lowest mark obtained by the student on the test was = 39
(b) We know that range = Highest marks – Lowest marks
= 95 – 39
= 56
(c) Mean of Marks is equal to = Sum of all the marks obtained by these groups of students divided by the Total Number of students
= (39 + 48 + 56 + 85 + 85 + 75 + 76 + 81+ 90 + 95) divided by 10
= 730/10
= 73
Question 5. The enrolment in a school during their six consecutive years is as follows:
1555, 1670, 1750, 2013, 2540 and 2820.
Find the mean enrolment of their school for this period.
Answer 5:
Mean enrolment is equal to = Sum of all observations divided by the number of observations
= (1555 + 1670 + 1750 + 2013 + 2540 + 2820)/ 6
= (12348/6)
= 2058
Hence, The final mean enrolment of the school for the given period is 2058.
Question 6. The heights of ten girls were measured in cm, and then the results are given as follows:
135, 150, 139, 146, 128, 151, 132,149, 143 and 141.
(a) What is the height found of the tallest girl?
(b) What is the height of the shortest girl?
(c) What is the range of the data?
(d) What is the mean height found of the girls?
(e) How many girls have heights that are more than the mean height?
Answer 6:
Firstly we will have to arrange the given data in ascending order,
= 128, 141, 143, 132, 135, 139, 146, 149, 150 and 151
(a) The height of the tallest girl is 151 cm
(b) The height of the shortest girl is 128 cm
(c) Range of given data is equal to = Tallest height – Shortest height
= 151 – 128
= 23 cm
(d) Mean height of the girls is equal to = Sum of the height of all the girls divided by the total number of girls present
= (128 + 132 + 143 + 135 + 139 + 141 +146 + 149 + 150
+ 151) divided by 10
= 1414/10
= 141.4 cm
(e) Five girls have heights which is more than the mean height (which is 141.4 cm).
Question 7. The scores in a mathematics test (out of 25) of the 15 students in a class are as follows:
19, 25, 10, 5, 16, 25, 23, 20, 9, 20, 15, 20, 24, 12 and 20
Find the Mode and the Median of this data. Are they the same?
Answer 7:
Arranging the following given scores in ascending order, we receive
5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25 and 25
Mode,
Mode is determined as the value of the variable which is present most frequently.
Clearly, the number 20 occurs the maximum number of times.
Hence, the Mode of these given sores is 20
Median is,
The value of that middle observation is called the median of the data.
Here the n = 15, which is odd.
There, n is the number of students present.
∴median is the = value of ½ (n + 1)the observation.
= ½ (15 + 1)
= ½ (16)
= 16/2
= 8
Then, the value of the 8th term = 20
So, the Median is the 20.
Yes, both values are the same.
Question 8. The runs scored in the cricket match by the 11 players are as follows:
6, 15, 80, 120, 50, 100, 10, 15, 8, 10 and 15
Find the Mean, Mode and the Median of this data. Are these three same?
Answer 8
Arranging the runs scored in the cricket match by these 11 players in ascending order, we receive
6, 8, 10, 10, 15, 15, 15, 50, 80, 100 and 120
Mean,
The mean of the given above data is given as = Sum of all of the observations divided by the total number of observations in the abovegiven data.
= (6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120) divided by 11
= 429/11
= 39
Mode,
Mode is determined as the value of the variable which is present most frequently.
So, Clearly, the number 15 occurs the maximum number of times.
Hence, the Mode of these given scores is 15
Median is,
The value of the middlemost observation of the data.
Here n = 11, which is an odd number.
Where n is the number of players.
Hence median is = value of ½ (n + 1)the observation.
= ½ (11 + 1)
= ½ (12)
= 12/2
= 6
Then, the value of the 6th term = 15
Hence, the Median is 15.
No, these three (mean, Median and Mode) are not the same.
Question 9. The weights (in kg.) of 15 students present in a class are:
38, 42, 43, 35, 37, 45, 50, 32, 43, 40, 36, 38, 43, 38 and 47
(i) Determine the Mode and Median of the above data.
(ii) Is there more than one Mode possible?
Answer 9
Arranging the abovegiven weights of 15 students present in the class in ascending order, we receive,
32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50
(i) Data’s Mode and Median
Mode,
Mode is determined as the value of the variable which is present most frequently.
S, Clearly, the number 38 and 43 both occurs three times.
Hence, the Mode of the given weights is both 38 and 43.
Median is,
The value of the middlemost observation of the data.
Here n = 15, which is an odd number.
Where n is the number of students.
Hence the median is equal to the value of ½ (n + 1) of the observation.
Which is equal to = ½ (15 + 1)
= ½ (16)
= 16/2
= 8
Now, the value of the 8th term = 40
Hence, the median will be 40.
(ii) Yes, there are two modes present for the given weights of the students.
Question 10. Find both the Mode and Median of the given data: 13, 14, 19, 16, 12, 12, 14, 13, 14
Answer 10:
Arranging the abovegiven data in ascending order, we receive
= 12, 12, 13, 13, 14, 14, 14, 16, 19
Mode is determined as the value of the variable which is present most frequently.
Clearly, the number 14 occurs a maximum number of times.
Hence, the Mode of this given data is found to be14.
Median is,
The value of the middlemost observation of the data.
Here n = 9, which is an odd number.
Where n denotes the number of students.
Hence, the median = value of ½ (9 + 1)the observation.
= ½ (9 + 1)
= ½ (10)
= 10/2
= 5
Then, the value of the 5th term = 14
Hence, the median is the number 14.
Question 11. Tell whether the following statement is true or false:
(a) The Mode is always present as one of the numbers in the given data.
Answer 11
The statement given above is true.
Because Mode,
Mode is determined as the value of the variable which is present most frequently.
Hence, the Mode is always one of the numbers present in the data.
(b) The Mean is one of the numbers present in the data.
Answer:
The above statement which is given above is false.
Because the Mean may or may not be the one of the numbers present in the data.
(c) The Median is always present as one of the numbers in the data.
Answer:
The statement given above is true.
Because the median is,
The value of the middlemost observation of the data while arranged in ascending or in descending order.
Hence, the median is always one of the numbers present in a data
(d) The data 6, 13, 9, 4, 3, 8, 9, and 12 have a mean of 9.
Answer:
Mean is equal to = Sum of all given observations divided by the total no of observations.
= (6 + 4 + 3 + 8 + 9 + 12 + 13 + 9) divided by 8
= (64/8)
= 8
Hence, the abovegiven statement is false.
Question 12. Tell whether these following statements are certain to happen, impossible to happen, or can happen but not certain.
(a) You are older today than yesterday.
Answer:
It is certain to happen.
(b) A tossed coin will land heads up.
Answer:
It can happen but not certain.
(c) A die, when tossed, shall land up with eight on its top.
Answer:
It is impossible as there are only six faces present on a die, and these faces are marked as the numbers 1, 2, 3, 4, 5, and 6.
(d) The next traffic light seen will be green.
Answer::
It can happen but not certain.
(e) Tomorrow will be a cloudy day.
Answer::
It can happen but not certain.
Question 13. There are six marbles present in a box ranging with numbers from 1 to 6 marked on each one of them.
(a) What is the major probability of drawing a marble with the number 2?
Answer::
From the above question, it is given that
There are six marbles in the box where numbers from 1 to 6 are marked.
The probability of drawing a marble with the number 2 is = the number of favourable outcomes divided by the number of possible outcomes
= (1/6)
(b) What is the major probability of drawing a marble with the number 5?
Answer:
From the above question, it is given that
There are six marbles in the box where numbers from 1 to 6 are marked.
Probability of drawing a marble with the number 5 = Number of favourable outcomes divided by the number of possible outcomes
= (1/6)
Question 14. A coin is flipped to decide which of the two teams starts the game. What is the probability that team A will start?
Answer:
A coin has two faces. One is named head, and the other one is named Tail.
Now, one team can choose either a Head or a Tail.
The probability of team A starting the first= number of favourable outcomes/
Number of possible outcomes
= ½
Question 15. Let x, y, and z denote three observations. The final Mean of these observations is
(i) (x × y × z)/3 (ii) (x + y + z)/3
(iii) (x – y – z)/3 (iv) (x × y + z)/3
Answer:
The correct answer is (ii) (x + y + z)/3
Explanation – The average or the Arithmetic Mean or the Mean of the given data is the Sum of all of these observations divided by the number of observations.
Question 16. The number of trees present in different parts of a city is 33, 48,33, 34, 33, 34, 33 and 24. The Mode of the following data is
(a) 24 (b) 34 (c) 33 (d) 48
Answer:
(c) 33
Explanation
Mode is the observation which occurs most frequently in the data.
Question 17. Which measures of the central tendency get affected in the extreme observations of both of these ends of a data arranged in the descending order are removed?
(i) Mean and mode (ii) Mean and Median
(iii) Mode and Median (iv) Mean, Median and Mode
Answer:
(i) Mean and Mode
Question 18. The range of these data is: 18, 12, 21, 6, 17, 8, 4, 13 is
(a) 17 (b) 12 (c) 8 (d) 15
Answer:
(a) 17
The major difference between the highest and the lowest observations in the given data is called its range.
The range is defined as = Highest – lowest
= 21 – 4
= 17
Question 19. The median of the following data: 3, 4, 5, 6, 7, 3, 4 is
(a) 5 (b) 3 (c) 4 (d) 6
Answer:
(c) 4
Explanation
When the given data is arranged in an ascending or descending order, then the middle observation present is known as the median of the data.
So, now arrange the given observation into an ascending order which is 3, 3, 4, 4, 5, 6, 7
Therefore, the number 4 is the middle observation, and it is the median of the abovegiven data.
Question 20. Out of these five brands of chocolates in the shop, a boy has to purchase the brand that is most liked by the children. What measure of the central tendency would be most appropriate if any of the given data is provided to him?
(a) Mean (b) Mode
(c) Median (d) Any of the three
Answer:
The correct option is (b) Mode
Explanation– Mode is the observation that frequently occurs in the data.
Question 21. On tossing a coin, the outcome generated is
(i) only head
(ii) only tail
(iii) neither head nor tail
(iv) either head or tail
Answer::
(d) either head or tail
Question 22. The Mean of three numbers is denoted as 40. All three numbers are different natural numbers. If the lowest number is 19, then what could be the highest possible number of the remaining two numbers?
(a) 81 (b) 40 (c) 100 (d) 71
Answer::
(a) 81
Explanation –
From the above question, it is given that,
The Mean of the three numbers is 40.
The lowest number is = 19
Let us assume that the other two numbers be P, Q.
Then,
The Mean = (P + Q + 19)/3
40 = (P + Q + 19)/3
By cross multiplication, we receive,
120 = P + Q + 19
120 – 19 = P + Q
Now, P + Q = 101
So, 81 + 20 = 101
Therefore, the highest number is 81
Question 23. Kajal earned scores of 97, 73 and 88, respectively, in her first three exams. So If she scored the number 80 in her fourth examination, then her average score becomes
(i) increased by 1 (ii) increased by 1.5
(iii) decreased by 1 (iv) decreased by 1.5
Answer::
(d) decreased by 1.5
Explanation
From the above question,
Kajal earned scores in her last 3 exam = 97, 73, 88
Then, the Mean would be = (97 + 73 + 88 +)/3
Mean = 86 marks
Kajal earned the score in her 4 exam = 97, 73, 88, 80
Then, Mean is = (97 + 73 + 88 + 80)/4
Mean = 84.5 marks
Then, her average score becomes 86 – 84.5 = 1.5, decreased by 1.5
Question 24. Which measure of the central tendency best represents the data of the most popular politician after their debate?
(i) Mean (ii) Median (iii) Mode (iv) Any of the above
Answer:
The correct answer is (c) Mode
Explanation – Mode is the observation that generally occurs most frequently in the data.
Question 25. Which of these following has the same mean, median and Mode?
(i) 6, 2, 5, 4, 3, 4, 1 (ii) 4, 2, 2, 1, 3, 2, 3
(iii) 2, 3, 7, 3, 8, 3, 2 (iv) 4, 3, 4, 3, 4, 6, 4
Answer:
the correct answer is (iv) 4, 3, 4, 3, 4, 6, 4
Explanation Mean of the given data is given as = (4 + 3 + 4 + 3 + 4 + 6 + 4)/7
= 4
Mode is the observation that generally occurs most frequently in the data, which is 4.
When the given data is arranged in an ascending or descending order, then the middle observation is said to be the median of the given data.
Arranging the given data as 3, 3, 4, 4, 4, 4, 6.
So, the Median is 4.
Questions 26. In the below Questions, fill in the following blanks to make the statements true.
 The major difference between the highest and lowest observations of a given data is called _________.
Answer::
The major difference between the highest and lowest observations of a given data is called range.
 The Mean of the data is known as _________.
Answer:
The average or the Arithmetic Mean or the Mean of a given data is known as the Sum of all the observations by the number of observations.
 In a set of observations, the observation that occurs most oftently is known as _________.
Answer:
As Mode
Mode is defined as the observation that occurs the most frequently in the given data.
 In a given data, arranged in any way, whether in an ascending or descending order, the middle of most of this observation is always called _________.
Answer:
It is known as the median.
When the given data is arranged in any way, whether in ascending (or descending) order, then the middle of most of this observation is always the median of the data.
 Mean, Median, Mode these are the measures of _________.
Answer:
Central tendency.
Mean, median and Mode these three are the representative values of a group of observations. They are also called as the measures of central tendency of the given data.
 The probability of an event which is almost certain to happen is _________.
Answer
The major probability of an event which is so certain to happen is 1.
 The major probability of an event which is almost impossible to happen is _________.
Answer:
The major probability of an event which is almost impossible to happen is 0.
 When a die is thrown, the major probability of getting any number less than 7 is _________.
Answer:
When a die is thrown, the major probability of getting any number less than 7 is 1.
Let us assume that the numbers 1, 2, 3, 4, 5 and the number 6 are the possible outcomes when a die is thrown.
The probability of receiving a number which is less than 7 is = number less than seven divided by the number of sides in the die.
= 6/6
= 1
 In throwing a die, the total number of possible outcomes coming is _________.
Answer
In throwing a die, the total number of possible outcomes which can be generated is 6.
 _________ can be used to compare the two collections of data.
Answer:
A double bar graph is majorly used to compare the two collections of data.
 The representation of data with the bars of uniform width is called _________.
Answer:
The representation of the data that is present in the form of rectangles or bars of uniform width is known as a bar graph.
 If the arithmetic means of the numbers 8, 4, x, 7, 6, 2, is 5, then what is the value of the symbol x is _________.
Answer:
If the arithmetic means of the numbers 8, 4, x, 7, 6, and 2 are 5, then the value of the symbol x is 3.
 The median of any data lies between the _________ and _________ observations.
Answer:
The median of any data always lies between the minimum and the maximum observations.
Benefits of Solving Important Questions Class 7 Mathematics Chapter 3
Practice is very important for students. It will help them to clear their concepts and build their ideas about the subject matter. Some students fear mathematics simply because they need help understanding the subject matter. Practice will help them to get the concepts easily. The Important Questions Class 7 Mathematics Chapter 3 prepared by the experts of Extramarks will help students in several ways. The benefits are
 Sometimes students need more than the textbook exercises. They must take help from other sources to take preparation to another level. The experts of Extramarks recognised this and prepared the question series to help students. They have collated the questions from sources such as the CBSE sample papers, NCERT exercises, Important reference books and NCERT exemplars. They have included a few questions from the CBSE past years’ question papers so that students may know which types of questions generally come in exams. Thus, the Mathematics Class 7 Chapter 3 Important Questions will help students practise.
 The experts have solved the questions too. They explained the questions and followed a stepbystep process to solve the questions. Experienced professionals have further checked the answers to ensure the best quality of the content. Thus, students can follow the Class 7 Mathematics Chapter 3 Important Questions if they need help solving the questions. They can check their answers with the experts’ answers. Thus, it will boost their confidence and generate interest in the subject matter.
 Practice is very important to score better in Mathematics. Many students fear mathematics simply because they don’t understand the subject matter. They must practice as much as possible because practice will help them clarify their doubts. The Chapter 3 Class 7 Mathematics Important Questions will help them to build their concepts and boost their confidence. It will generate interest in the subject matter. Thus, students can score better in exams.
Extramarks is a leading company that provides all the study materials related to NCERT and CBSE. You can register on our official website and download these study materials. We provide the CBSE syllabus, CBSE sample papers, CBSE extra questions, CBSE revision notes, NCERT books, NCERT solutions, important questions, NCERT exemplar, vital formulas and many more. Like the Important Questions Class 7 Mathematics Chapter 3, you will also find important questions for other chapters. Links to the study materials are given below
 NCERT books
 Important questions
 CBSE Revision Notes
 CBSE syllabus
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 Important formulas
 CBSE extra questions
Q.1 Probability of any event always lies between _____________.
Marks:1
1. 0 and 1
2. 1 and 2
3. 2 and 3
4. 3 and 4
Ans
1. 0 and 1
Explanation
Probability always lies between 0 and 1.
Q.2 When a coin is thrown, then the probability of getting head is ______________.
Marks:1
0
$\frac{1}{4}$
$\frac{1}{2}$
1
Ans 3.
$\frac{1}{2}$
Explanation
When s coin is thrown, it has two possible outcomes i.e. Head or Tail
Therefore, the required probability =
$\frac{1}{2}$
Q.3 The heights of 15 students are given below:
165, 155, 168, 160, 163, 162, 165, 168, 156, 159, 160, 164, 163, 165, 160.
Find:
(i) the range of heights
(ii) the mode
(iii) the median
Marks:3
Ans
Arranging in ascending order 155, 156, 159, 160, 160, 160, 162, 163, 163, 164, 165, 165, 165, 168, 168
(i) Range = 168 – 155 = 13
(ii) Mode = 160 and 165 occurs 3 times. Therefore, modes are 160 and 165 both.
(iii) Median = 163 (central value)
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FAQs (Frequently Asked Questions)
1. What are the main concepts of Class 7 Mathematics Chapter 3?
Chapter 3 of Class 7 Mathematics is about data handling. In this chapter, students will learn about data collection and organisation. They will also learn about mean, median, mode and probability. They must follow the textbook exercises sincerely because they will need the concepts in later classes. They can easily understand the chapter clearly because the textbook has explained the concepts interestingly. They can also take help from the Important Questions Class 7 Mathematics Chapter 3 prepared by the experts of Extramarks.
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