class 8 maths chapter 5 deals with data handling.
Exercises and solutions of Data Handling available here so students can read online view.
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Find solutions to exercise 5.1, exercise 5.2 and 5.3 in chapter 5 in class 8 maths.
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solutions for exercises in data handling class 8
Solution to exercise 5.1 (1) data handling class 8
Solution to exercise 5.1 (2) data handling class 8
ncert solutions for class 8 maths chapter 5 exercise 5.1
exercise 5.1 (1)
For which of these would you use a histogram to show the data?
(a) The number of letters for different areas in a postman’s bag.
(b) The height of competitors in an athletics meet.
(c) The number of cassettes produced by 5 companies.
(d) The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station
Give reasons for each.
Solution to exercise 5.1 (1) data handling class 8
Histogram is a graphical representation of data, if data represented in manner of class-interval.
In case (b) and (d), we use a histogram to show the data, because in these cases, data can be divided into class-intervals.
In case (b), a group of competitions having different heights in an athletics meet In case (d), the number of passengers boarding trains in an interval of one hour at a station.
exercise 5.1 (2)
The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning:
W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W W M W G W M G W M M B G G W
Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.
Solution to exercise 5.1 (2) data handling class 8
The illustrate of data by bar-graph is as follows.
Exercise 5.1 (3)
3 The weekly wages (in Rs) of 30 workers in a factory are.
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840
Using tally marks make a frequency table with intervals as 800–810, 810–820 and so on.
Solution to exercise 5.1 (3) data handling class 8
Exercise 5.1 (4)
4 Draw a histogram for the frequency table made for the data in Question 3, and answer the following questions.
(i) Which group has the maximum number of workers?
(ii) How many workers earn Rs 850 and more?
(iii) How many workers earn less than Rs 850?
Solution to exercise 5.1 (4) data handling class 8
(i) 830 – 840 group has the maximum number of workers
(ii) 10 workers can earn more than Rs 850.
(iii) 20 workers earn less than Rs 850.
Exercise 5.1 (5)
5 The number of hours for which students of a particular class watched television during holidaysis shown through the given graph.
Answer the following.
(i) For how many hours did the maximum number of students watch TV?
(ii) How many students watched TV for less than 4 hours?
(iii) How many students spent more than 5 hours in watching TV?
Solution to exercise 5.1 (5) data handling class 8
(i) The maximum number of students watched TV. for 4 – 5 hours.
(ii) 34 students watched T.V. for less than 4 hours.
(iii) 14 students spent more than 5 hours in watching T.V.
ncert solutions for class 8 maths chapter 5 exercise 5.2
Exercise 5.2 (1)
1. A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey.
From this pie chart answer the following:
(i) If 20 people liked classical music, how many young people were surveyed?
(ii) Which type of music is liked by the maximum number of people?
(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?
Solution to exercise 5.2 (1) data handling class 8
(i) Given 20 people liked classical music.
In figure classical music percentage is 10%.
So 10%=20 people.
Then 100%=200 people.
∴ 200 young people were surveyed.
(ii) Light music is liked by the maximum number of people.
(iii) Given a cassette company were to make 1000 CD’s.
CD’s of semi-classical music=
(²⁰/₁₀₀)×1000=200
CD’s of light music=(⁴⁰/₁₀₀)×1000=400
CD’s of folk music=(³⁰/₁₀₀)×1000=300
Exercise 5.2 (2)
2. A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.
(i) Which season got the most votes?
(ii) Find the central angle of each sector.
(iii) Draw a pie chart to show this information.
Solution to exercise 5.2 (2) data handling class 8
(i) Winter season got more votes.
(ii) Total votes=90+120+150=360.
Central angle of summer season=number of votes ÷total votes=(⁹⁰/₃₆₀)× 360°=90°
Central angle of Rainy season=
(¹²⁰/₃₆₀)×360°=120°
Central angle of winter season=
(¹⁵⁰/₃₆₀)×360°=150°
(iii)
Exercise 5.2 (3)
3 Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.
Solution to exercise 5.2 (3) data handling class 8
Here central angle=360°, Total number of people=36.
Exercise 5.2 (4)
4 The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.
(i) In which subject did the student score 105 marks? (Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?)
(ii) How many more marks were obtained by the student in Mathematics than in Hindi?
(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi. (Hint: Just study the central angles).
Solution to exercise 5.2 (4) data handling class 8
(i)The student scored 105 marks in Hindi.
(ii)Marks obtained in Mathematics = 135 Marks obtained in Hindi = 105
Difference = 135 – 105 = 30
Thus, 30 more marks were obtained by the student in Mathematics than in Hindi.
(iii) The sum of marks in Social Science and Mathematics = 97.5 + 135 = 232.5
The sum of marks in Science and Hindi = 120 + 105 = 225
Yes, the sum of the marks in Social Science and Mathematics is more than that in Science and Hindi.
Exercise 5.2 (5)
5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.
Solution to exercise 5.2 (5) data handling class 8
Total number of students=72.
ncert solutions for class 8 maths chapter 5 exercise 5.3
Exercise 5.3
Exercise 5.3 (1)
1 List the outcomes you can see in these experiments.
(a) Spinning a wheel (b) Tossing two coins together.
Solution to exercise 5.3 (1) data handling class 8
(a) There are four letters A, B, C And D in a spinning wheel. So there are 4 outcomes.
(b) When two coins are tossed together. There are four possible outcomes HH, HT, TH, TT.
(Here HT means head on first coin and tail on second coin and so on.)
Exercise 5.3 (2)
2 When a die is thrown, list the outcomes of an event of getting
(i) (a) a prime number (b) not a prime number.
(ii) (a) a number greater than 5 (b) a number not greater than 5.
Solution to exercise 5.3 (2) data handling class 8
(i) (a) Outcomes of event of getting a prime number are 2, 3 and 5.
(b) Outcomes of event of not getting a prime number are 1, 4 and 6.
(ii)(a) Outcomes of event of getting a number greater than 5 is 6
(b) Outcomes of event of not getting a number greater than 5 are 1, 2, 3, 4 and 5
Exercise 5.3 (3)
3 Find the.
(a) Probability of the pointer stopping on D in (Question 1-(a))?
(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?
(c) Probability of getting a red apple. (See figure below)
Solution to exercise 5.3 (3) data handling class 8
(a) In a spinning wheel, there are five pointers A, A, B, C, D. So there are five outcomes. Pointer stops at D which is one outcome. So the probability of the pointer stopping on D=¹/₅
(b) There are 4 aces in a deck of 52 playing cards. So, there are four events of getting an ace.
So, probability of getting an ace = ⁴/₄₂=¼.
(c) Total number of apples = 7 Number of red apples = 4
Probability of getting red apple =⁴/₇
Exercise 5.3 (4)
4 Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of .
(i) getting a number 6?
(ii) getting a number less than 6?
(iii) getting a number greater than 6?
(iv) getting a 1-digit number?
Solution to exercise 5.3 (4) data handling class 8
Given that numbers 1 to 10 are written on ten separate slips
(i) Outcome of getting a number 6 from ten separate slips is one.
∴ Probability of getting a number 6 =¹/₁₀
(ii) Numbers less than 6 are 1, 2, 3, 4 and 5 which are five. So there are 5 outcomes.
∴ probability of getting a number less than 6 = ⁵/₁₀=½
(iii) Number greater than 6 out of ten that are 7, 8, 9, 10. So there are 4 possible outcomes
∴ Probability of getting a number greater than 6 =⁴/₁₀=⅖
(iv) One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 out of ten. There are 9 favourable out comes.
∴ Probability of getting a 1-digit number=⁹/₁₀
Exercise 5.3 (5)
5 If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?
Solution to exercise 5.3 (5) data handling class 8
There are five sectors. Three sectors are green one sector is blue and one sector red.
∴ Probability of getting green sector=⅗
There is one blue sector out of five sectors. Non-blue sectors = 5 -1= 4 sectors
∴ Probability of getting a non-blue sector=⅘
Exercise 5.3 (6)
6 Find the probabilities of the events given in Question 2.
Solution to exercise 5.3 (6) data handling class 8
In question 2 given that a die is thrown, then total possible outcomes=6
(i) (a) On that die 2,3 and 5 are prime numbers. And 1,4 and 6 are not prime numbers.
To get prime numbers there are three possible outcomes.
Probability of getting a prime number =³/₆= ½
(b) 1, 4, 6 are not the prime numbers. So there are 3 outcomes out of 6.
Probability of getting a number which is not prime = ³/₆=½
(ii)(a) Only 6 is greater than 5. So there is one outcome out of 6.
Probability of getting a number greater than 5 = ⅙
(b) Numbers not greater than 5 are 1, 2, 3, 4 and 5. So there are 5 outcomes out of 6.
Probability of getting a number not greater than 5 = ⅚
data handling class 8
1. Data mostly available to us in an unorganised form is called raw data.
2. In order to draw meaningful inferences from any data, we need to organise the data systematically.
3. Frequency gives the number of times that a particular entry occurs
4. Raw data can be ‘grouped’ and presented systematically through ‘grouped frequency distribution’
5. Grouped data can be presented using histogram. Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval. Also, there is no gap between the bars as there is no gap between the class intervals.
6. Data can also presented using circle graph or pie chart. A circle graph shows the relationship between a whole and its part.
7. There are certain experiments whose outcomes have an equal chance of occurring.
8. A random experiment is one whose outcome cannot be predicted exactly in advance
9. Outcomes of an experiment are equally likely if each has the same chance of occurring.
One or more outcomes of an experiment make an event. Chances and probability are related to real life.