Chapter 5

Data Handling

Data handling is essential for eighth-grade students to clear their doubts and perform well in exams. Students can use these solutions to obtain a better knowledge of the subject. MSVGo provides these NCERT solutions to help students solve problems and gain a better understanding of related disciplines and overcome their fear of mathematics. 

Students can also view the NCERT Class 8 Maths Solutions for Data Handling Chapter 5 online or download the PDF version by following the links. 

Data management is an important concept for maintaining the integrity of research data. Whatever subject we are studying, we have data in the form of a numerical figure. Observation is the name given to each value of this kind. 

Data is the term used to describe the collection of all observations. To handle what is referred to as data, a variety of data management strategies are employed, which will be discussed in this chapter and succeeding classes. Subject experts created these data handling solutions in compliance with the CBSE syllabus for 2022–22, as mandated by the board.

Exercise questions 5.1

Page 76

Question 1. For which of these would you use a histogram to depict 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 five companies.

(d) The number of passengers boarding trains from 7.00 am to 7.00 pm at a station.

Give reasons for each.

Answer. 

If the data uses class intervals, a histogram can provide an accurate representation. 

As the examples in choices (b) and (d) may be separated into class intervals, the data can be displayed using a histogram. 

As the cases in choices (a) and (c) cannot be broken down into class intervals, the data cannot be shown in a histogram.

Question 2. The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B), or girl (G). The following is a list of the shoppers during the first hour in the morning:

WWWGBWWMGGMMWWWWGBMWBGGMWWMMWW WMWBWGMWWWWGWMMWWMWGWMGWMMBGGW

Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

Answer.

Shopper

Tally marks

No. of shoppers

W

|||| |||| |||| |||| |||| |||

28

M

|||| |||| |||| 

15

B

|||| 

5

G

|||| |||| ||

12

Total

-

60

Question 3. The weekly wages (in ₹) 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, and 840. Using tally marks, make a frequency table with intervals of 800–810, 810–820, and so on.

Answer.

The following is a frequency table with intervals of 800–810, 810–820, and so on, using tally marks:

Class intervals

Tally marks

Frequency

800–810

|||

3

810–820

||

2

820–830

|

1

830–840

|||| ||||

9

840–850

||||

5

850–860

|

1

860–870

|||

3

870–880

|

1

880–890

|

1

890–900

||||

4

Total

-

30

Question 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 workers?

(ii) How many workers earn ₹ 850 and more?

(iii) How many workers earn less than ₹ 850?

Answer.

(i) 830–840 is the group with the most workers, nine, in comparison to the other groups. 

(ii) Employees earning  ₹ 850 or more per year = 1 + 3 + 1+ 1+ 4 = 10 

(iii) Employees earning less than ₹ 850 = 3 + 2 + 1 + 9 + 5 = 20

Question 5. The number of hours for which students of a particular class watched television during holidays is shown through the given graph. Answer the following.

(i) For how many hours did the maximum students watch TV?

(ii) How many students watched TV for less than four hours?

(iii) How many students spent more than five hours watching TV?

Answer. 

(i) For four to five hours, 32 pupils watched TV. The maximum number of students who sat in front of the TV for four to five hours was 400. 

(ii) The percentage of students who watched fewer than four hours of TV equals 22 + 8 + 4 = 34. 

(iii) The percentage of pupils who spent more than five hours watching TV equals 8 + 6 = 14.

Page 82

Question 1. A survey was conducted to identify the type of music that a certain group of young people in a city liked. The pie chart shows the findings of this survey.

Based on 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 majority of the people?

(iii) If a cassette company were to make 1,000 CDs, how many of each type would they make?

Answer. 

(i) Ten percent equals 100 people; 20% equals (100 x 20)/10 = 200; 200 people were surveyed.

(ii) Given that 40% of all respondents rated light music as their favourite genre, and no other type of song received a higher rating, we can assume that light music is the most popular. 

(iii) CDs of classical music equals (10 x 1,000)/100 = 100; CDs of semi-classical music equals (20 x 1,000)/100 = 200; CDs of light music equals (40 x 1,000)/100 = 400; CDs of folk music equals (30 x 1,000)/100 = 300.

Question 2. A group of 360 people were asked to vote for their favourite season: monsoon, 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.

Answer. 

(i) Winter received the most votes according to the table. 

(ii) Summer’s central angle equals (90 x 360)/ 360 = 90o 

Monsoon’s central angle is equal to (120 x 360)/360 = 120o. 

Winter’s central angle is equal to (150 x 360)/360 = 150o.

(iii)

Question 3. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.

 

Answer. 

Here, the central angle is 360°, and the total number of people is 36.

 

 

Question 4. The pie chart displays a student’s marks in Hindi, English, Mathematics, Social Science, and Science. If the student’s total marks 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 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).

Answer. 

(i) In Hindi, the student scored 105 marks. 

(ii) The number of marks earned in mathematics is 135; the marks earned in Hindi are 105. The difference is equal to 135 - 105 = 30. 

As a result, the student received 30 more marks in mathematics than in Hindi. 

(iii) A total of 97.5 and 135 marks in Social Science and Mathematics equals 232.5 marks. The total of 120 marks in Science and 105 marks in Hindi is 225 marks. 

It is true that the total of the marks in Social Science and Mathematics is higher than the total of the marks in Science and Hindi.

Question 5. The number of students in a hostel speaking different languages is given below. Display the data in a pie chart.

Answer.

 

Page 87

Question 1. List the outcomes you can see in these experiments.

(a) Spinning a wheel (b) Tossing two coins together

Answer. 

(a) A spinning wheel has the letters A, B, C, and D arranged in a circle. As a result, there are four possible outcomes. 

(b) When two coins are flung together, there are four possible outcomes: HH, HT, TH, and TT.

Question 2. When a die is thrown, list the probabilities of getting

(i) (a) a prime number (b) not a prime number.

(ii) (a) a number greater than five (b) a number not greater than five.

Answer. 

(i) (a) The numbers 2, 3, and 5 are the outcomes of the event of receiving a prime number. 

(b) The numbers 1, 4, and 6 are the outcomes of not attaining a prime number. 

(ii) (a) In the event of receiving a number greater than 5, the outcome is 6. 

(a) The following are the outcomes of not getting a number bigger than 5: 1, 2, 3, 4, and 5.

Question 3. Determine the probability of:

(a) the pointer stopping on D in [Question 1-(a)].

(b) getting an ace from a well-shuffled deck of 52 playing cards.

(c) getting a red apple. (See figure below)

Answer. 

(a) There are five pointers on a spinning wheel labelled A, A, B, C, and D. So, there are five outcomes. One possible consequence is that the pointer comes to a halt at D. 

As a result, the likelihood of the pointer stopping on D is 1/5. 

(b) A standard 52-card deck contains four aces. As a result, there are four possible circumstances that result in an ace. So, the chance of getting an ace is 4/52 = 1/13

c) There are seven apples in total. The number of red apples is four. The likelihood of receiving a red apple is 4/7.

 

  • Raw data refers to the majority of data that is available to us in an unstructured state. 

  • Any data must first be organised methodically before it can be used to make helpful decisions. 

  • The frequency column shows how often a particular entry appears. 

  • Raw data can be "grouped" and shown in a systematic fashion using a "grouped frequency distribution."

  • A histogram is a visual representation of grouped data. The histogram is a type of bar graph in which the horizontal axis represents the class intervals and the bar heights represent the frequency of the class intervals. Furthermore, there is no space between the bars, just as there is no gap between the class intervals. 

  • A circle graph or a pie chart can also be used to display data. The relationship between an entity and its constituents is depicted in a circle graph. 

  • Certain experiments have a 50/50 chance of succeeding. 

  • The outcome of a random experiment cannot be predicted exactly. 

  • If each experiment's outcome had the same chance of occurring, they would all be equally likely. The number of alternative possibilities equals the probability of an event occurring. In an experiment with all possible outcomes being equally likely, the total number of possible outcomes is the entire number of possible outcomes. 

  • The result of an experiment, or a series of results, is referred to as an "event."

  • Probability and chance are real-world concepts.

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