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.

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

In (b) and (d),histograms can be drawn because data can be divided into class intervals.

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.

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

Arrangement of data in a table using tally marks is done as :

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, 806,840.

Using tally marks make a frequency table with intervals as 800-810, 810-820 and so on.

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

Grouped frequency table is made as follows:

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 ₹ 850 and more?

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

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

Histogram for the given data in question 3 is shown as:

From the above histogram, clearly we see that,

(i) The group 830-840 has the maximum number of workers i.e, 9.

(ii) The number of workers who earn equal and more than ₹ 850 are 1 + 3 + 1 + 1 + 4, i.e., 10.

(iii) The number of workers who earn less than ? 850 are 3 + 2 + 1 + 9 + 5, i.e., 20.

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 questions.

(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 watching TV?

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

We can observe the following from the given figure:

(i) The maximum number of students who watched TV for 4 to 5 hours is 32.

(ii) 4 + 8 + 22 = 34 students watched TV for less than 4 hours.

(iii)The number of students who watched TV for more than 5 hours is 8 + 6 = 14.

1.A survey was made to find the type of music that a certain group of young people liked in a city. The 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 CDs. How many of each type would they make?

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

(i) let, the number of young people surveyed =x

∴10% of x=20

\(\Rightarrow \frac { 100\times x}{ 10 } = 20 \)

\(\Rightarrow x=200\)

Thus, number of young people surveyed = 200

(ii) Light music is liked by the maximum people, i.e., 40%

(iii) Total number of CD = 1000

Number of CD’s in respect of:

classical music =\( \frac { 10\times 1000 }{ 100 } = 100\)

semi-classical music = \(\frac { 20\times 1000 }{ 100 } = 200\)

light music = \(\frac { 40\times 1000 }{ 100 } = 400\)

folk music = \(\frac { 30\times 1000 }{ 100 } = 300\)

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.

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

(i) Winter season got the maximum votes, i.e. 150.

(iii) Pie chart for the given data:

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

Find the proportion of each sector. For example, Blue is \(\frac { 18 }{ 36 } =\frac { 1 }{ 2 }\) ; Green is \(\frac { 9 }{ 36 } =\frac { 1 }{ 4 }\) and so on.

Use this to find the corresponding angles.

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

Central angles with their color are:

Blue colour:
\(=\left( \frac { 18 }{ 36 } \times 360 \right) ^{ \circ }=180^{ \circ }\)

Green colour:
\(=\left( \frac { 9 }{ 36 } \times 360 \right) ^{ \circ }=90^{ \circ }\)

Red colour:
\(=\left( \frac { 6 }{ 36 } \times 360 \right) ^{ \circ }=60^{ \circ }\)

Yellow colour:
\(=\left( \frac { 3 }{ 36 } \times 360 \right) ^{ \circ }=30^{ \circ }\)

Now, various components is shown by the adjoining pie chart.

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?

(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.

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

(i) For 540 marks, the central angle = \( 360^{ \circ}\)

∴ the central angle for 1 mark = \(\left( \frac { 360 }{ 540 } \right) ^{ \circ }=\left( \frac { 2 }{ 3 } \right) ^{ \circ }\)

∴ the central angle for 105 marks =\( \left( \frac { 2 }{ 3 } \times 105 \right) ^{ \circ }=70^{ \circ }\)

Hence, from the given pie chart, the subject is Hindi.

(ii) Difference between the central angles made by the subject of Mathematics and Hindi= \(90^{\circ} – 70^{\circ} = 20^{\circ}\).

Marks obtained for the central angle of \(360^{\circ}\), = 540
Marks obtained for the central angle of \(1^{\circ}\)=\(\frac { 540 }{ 360 } =\frac { 3 }{ 2 }\)

Marks obtained for the central angle of \(20^{\circ}=\frac { 3 }{ 2 } \times 20=30\)

Hence, the student obtained 30 more marks in Mathematics than Hindi.

(iii) Sum of the central angles made by Social Science and Mathematics =\( 65^{\circ}+ 90^{\circ} = 155^{\circ}\).

And, the sum of the central angles made by Science and Hindi = \(80^{\circ}+ 70^{\circ} = 150^{\circ}\).

Since \(155^{\circ} >150^{\circ}\), therefore, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

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

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

Let us find the central angle of each sector with the total scale = 72. We thus have the following table :

And the pie chart for the given data is:

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

(i) Spinning a wheel

(ii) Tossing two coins together

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

(i) We can get the possible outcomes on spinning the given wheel as B, C, D, E and A.

(ii) When two coins are tossed together, we get the following possible outcomes

HH, HT, TH, TT

.

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

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

In a throw of die, list of the outcomes of an event of getting

(i) (a) the prime number are 2, 3 and 5

(b) not a prime number are 1, 4 and 6

(ii) (a) a number greater than 5 = 6

(b) a number not greater than 5 are 1, 2, 3, 4, 5

3. Find the

(i) Probability of the pointer stopping on D in (Question 1-(a))?

(ii) Probability of getting an ace from a well-shuffled deck of 52 playing cards?

(iii) Probability of getting a red apple, (see figure below)

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

(i) Refer to fig. Question 1-(a)

Total number of sectors = 5

Number of sectors where the pointer stops at D = 1, because there is only one ‘D’ on the spinning wheel.

Probability of pointer stopping at D = \(\frac{1}5\)

(ii) Number of aces = 4 (one from each suit i.e. heart, diamond, club and spade)

Total number of playing cards = 52

Probability of getting an ace=\(\frac{Number\; of\; aces}{Total\; number\; of \;playing \;cards}\)

\(=\frac{4}{52}=\frac{1}{13}\)

(iii) Total number of apples = 7

Number of red apples = 4

Probability of getting red apples=\(\frac{Number \;of\; red \;apples}{Total \;number\; of \;apples}=\frac{4}7\)

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?

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

(i)An event of getting a number 6, i. e., if we obtain a slip having number 6 as an outcome out of total 10 slips

So favourable number of outcomes = 1

∴ required probability of getting a number 6 = \(\frac{1}{10}\)

(ii) Probability of getting a number less than 6 = \(\frac{5}{10}= \frac{1}2\) [∵ Numbers less than 6 are 1, 2, 3, 4, 5]

(iii) Probability of getting a number greater than 6 = \(\frac{4}{10}= \frac{2}5\) [∵ Number greater than 6 are 7, 8, 9, 10]

(iv) Probability of getting a 1-digit number = \(\frac{9}{10}\)
[∵ 1-digit numbers are 9, i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9]

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?

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

Out of the total 5 sectors, the pointer can stop at any of the sectors in 5 ways.

∴ Total number of outcomes = 5

There are 3 green sectors in the spinning wheel, out of which one can be obtained in 3 ways.
∴ Favourable number of outcomes = 3

So, the required probability for green sector= \(\frac { 3 }{ 5 }\)

Further, there are 4 ways to obtain a non-blue sector out of 4 non-blue present in the spinning wheel.

So, the required probability for non- blue sector = \(\frac { 4 }{ 5 } \)

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

Answer :

In a single throw of a die, we can get any one of the six numbers marked on its six faces.
Therefore, the total number of outcomes = 6

(i) Let A denote the event “getting a prime number”. So,event A occurs if we obtain 2, 3, 5 as an outcome.

∴ Favourable number of outcomes = 3

Hence, P\(\left( A \right) =\frac { 3 }{ 6 } =\frac { 1 }{ 2 } \)

(ii) Let A denote the event “not getting a prime number”. So, event A occurs if we obtain 1, 4, 6 as an outcome.

∴ Favourable number of outcomes = 3

Hence, P\(\left( A \right) =\frac { 3 }{ 6 } =\frac { 1 }{ 2 }\)

(iii) The event “getting a number greater than 5” will occur if we obtain the number 6.

∴ Favourable number of outcomes = 1

Hence, the required probability = \(\frac { 1}{ 6 } \)

(iv) The event “getting a number not greater than 5” will occur if we obtain one of the numbers 1, 2, 3, 4, 5.

∴ Favourable number of outcomes = 5

Hence, required probability = \(\frac { 5 }{ 6 } \)

There are total 16 questions present in ncert solutions for class 8 maths chapter 5 data handling

There are total 2 long question/answers in ncert solutions for class 8 maths chapter 5 data handling

There are total 3 exercise present in ncert solutions for class 8 maths chapter 5 data handling