Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling NOTE: THE CONCEPT MAP AND ALL THE EXERCISE QUESTIONS TO BE SOLVED IN THE NOTEBOOK.

Concept Map

Important points:

❖ Data: - Information especially facts or numbers, collected for use is called data. Each numerical fact is called an observation.

❖ Raw data: - The numerical data recorded in its original form, in an unorganized and random manner is called raw data.

❖ Array: - The raw data arranged in ascending or descending order of magnitude is called array. ❖ Range: - The difference between the largest and the smallest observed value in a set of data is

called the range of data. ❖ Frequency: - In a given set of data, the number of times a particular observation occurs is called

its frequency. ❖ To draw meaningful inferences from the given raw data, we need to organize it in the form of a

frequency distribution table. ❖ Frequency distribution: - A tabular arrangement of given numerical data showing the frequency

of each observation is called a frequency distribution and the table itself is called frequency distribution table.

❖ If the number of observations in a data is large and the difference between the highest and the

least observation is large, then the data is condensed into convenient number of groups called

classes. We record the frequency of observations falling in each group.

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling

❖ Frequency distribution of grouped data: - A tabular arrangement of given numerical data

showing the classes together with their corresponding frequencies is called a frequency

distribution of grouped data.

❖ Class Interval: - Each group into which the raw data is condensed is known as class interval (C.I.).

For example: 0 – 5, 5 – 10, 10 – 15, 15 – 20, etc.

❖ Class limits: - The end numbers of a class interval are called class limits. The smaller number is

the lower class limit and the larger number is the upper class limit. For example, in C.I 0 – 5, 0 is

the lower limit and 5 is the upper limit.

❖ Class size (or width): - The difference between the upper limit and the lower limit of a class is

known as its class size. For example, in C.I. 10 – 15, the class size= upper limit – lower limit= 15-

10 = 5.

❖ Class mark: - The class mark is the mid- point of the class interval.

Class mark = (upper limit + lower limit)/2

❖ The frequency distribution in which the upper limit of one class is the lower limit of the next

class is called an exclusive form.

❖ Representation of data graphically- i). Bar graph and ii). Histogram.

❖ I). Bar Graph: - A bar graph is a pictorial representation of the ungrouped numerical data. A

double bar graph is a bar graph showing two sets of data simultaneously.

❖ II). Histogram: - A histogram is a graphical representation of a grouped frequency distribution of

data. It is simply a bar graph in which the bars are adjacent.

❖ Difference between bar graph and histogram: - In a bar graph the height of each bar matters ad

not its width. It is therefore one-dimensional. In a histogram the width as well as the height of

each rectangle (bar) matters because the areas of the rectangles are proportional to the

corresponding class frequencies. Therefore, a histogram is two-dimensional.

❖ Pie Chart: -A pie chart is a circular diagram in which the components (observations) are

represented by the sectors of a circle. The size of each sector is proportional to the magnitude

of the component (observation) it represents.

❖ Central Angle for a component:-

❖ Probability: - The probability of an event is the measure of the chance of it occurring. It varies

from 0 to 1.

❖ Experiment: -An operation which produces well-defined outcomes is called an experiment.

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling

❖ Random experiment: -An experiment, which when repeated under identical conditions, does

not produce the same result or outcome every time, is known as a random experiment.

❖ Trial: - Performing a random experiment is called a trial.

❖ Outcome: -A result of some activity or experiment is known as its outcome.

❖ Event: - The collection of some or all possible outcomes of an activity or an experiment is called

an event.

❖ Probability of an occurrence of an event: -Let E be an event. Then, probability of an event P(E)

is defined as

Exercise 5A 1. The savings of six friends are given below: ₹1225, ₹1250, ₹1240, ₹1250, ₹1250, ₹1245 i). What is the highest saving? ii). What is the lowest saving? iii). What is the range? Ans1- i). ₹1250 is the highest saving. ii). ₹1225 is the lowest saving. iii). Range = Highest value – lowest value = 1250-1225= ₹25 3. (Refer to textbook for data) Array the data and form a frequency distribution table. i). What is the highest mark? ii). What is the range of marks? iii). Which mark is obtained by most of the students? Ans-3 Frequency Distribution Table-

Data Tally Marks Frequency

0 II 2

1 IIII 4

2 5

3 II 7

4 I 6

5 IIII 4

6 III 3

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling

7 IIII 4

8 III 3

9 II 2

Total 30

i). Highest mark = 9 ii). lowest mark = 0 Range = 9- 0= 9 iii). Highest frequency/mark which occurs most number of times= 3 *Solve Q.2 using the same method.

Exercise 5B

1. Construct a frequency distribution table for the data given (Refer to textbook for data). Ans1- Frequency Distribution Table-

Class Interval (C.I.) Tally Marks Frequency

3 – 6 I 1

6 – 9 5

9 -12 IIII 4

12 – 15 IIII 4

15 – 18 II 7

18 – 21 III 3

21 – 24 I 6

Total 30

2. Form a frequency distribution table with grouping 10 – 20, 20 – 30, 30 – 40 and so on. (Refer to textbook for data). Ans-2 Frequency Distribution Table-

Class Interval (C.I.) Tally Marks Frequency

10 – 20 I 11

20 – 30 III 13

30 – 40 III 13

40 – 50 IIII 9

50 – 60 IIII 4

Total 50

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling 4. Study the table (refer to textbook) and answer the following questions: - i). What is the class size? Ans – 10 ii). What is the lower limit of the last class? Ans– 70 iii). What is the upper limit of the class with the highest frequency? Ans– 24 iv). How many students obtained ≥ 50 marks? Ans – (18 +10+7) = 35 v). How many students scored less than 40 marks? Ans– (3+5+8+24) = 40 vi). What is the total number of students who took the test? Ans – (3+5+8+24+21+18+10+7) = 96 vii). What percentage of students obtained marks more than or equal to 30 but less than 40?

Ans- 24

96× 100% = 25%

5. Study the frequency distribution table (refer to textbook) and answer the following questions: - i). In which interval is the greatest frequency found? Ans – 1000 – 1500 ii). How many shops have their daily profits ranging from ₹1500 to ₹1999? Ans – 20 iii). How many shops earn a daily profit of ₹2000 or more? Ans – 17+ 6 = 23 iv). What percentage of shop have their daily profit below ₹2000? Ans- No. of shops which have their daily profit below ₹2000= 12 +18+ 27+ 20= 77

Percentage= 77

100× 100% = 77%

v). What is the average profit of the shops earning the highest daily profit?

Ans- Average = (2500+3000)

2=

5500

2= ₹2750

*Solve Q.3 using the same method.

Exercise 5C

1.

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling

Ans-

2. Read the bar graph given in figure 1 and answer the following questions: -

0

200

400

600

800

1000

1200

1400

1951 1961 1971 1981 1991 2001 2011

Po

pu

lati

on

(in

mill

ion

s)

Year of census

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling

i). Which course has the most students enrolled in it? Ans- Economics ii). How many times the enrollment in Economics is more than the enrollment in Chemistry? Ans- 300-175= 175; 2 times iii). How many students are enrolled in the course with most students? Ans- 350 in Economics iv). How many students are enrolled for Economics than for Physics? Ans- 350 – 150 = 200 v). Name the two subjects for which equal number of students are enrolled. Ans- English and Psychology with 250 students. vi). What is the ratio of the number of students enrolled for Chemistry to the number of students for Physics? Ans- Ratio= Number of students for Chemistry: No. of students for Physics= 175:150= 7:6 3. Read the double bar graph given in Fig.2 and answer the following questions:

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling i). What information is given by the double bar graph? Ans- Pass percentage for classes X and XII for the years 2015 to 2019. ii). In which year is the pass percentage of Class X maximum? Ans- 2016 iii). In which year is the pass percentage of Class X more as compared to Class XII? Ans- 2016 iv). In which year is the difference between the pass percentage of Class X and Class XII minimum? Ans- 2018 v). Find the average pass percentage of Class XII and Class X in five years. Which class has the higher average pass percentage? Ans- Average pass percentage for Class XII= (84+85+87+90+92)/5 = 438/5 = 87.6% Average pass percentage for Class X= (80+90+82+87+85)/5 = 424/5 = 84.8% Class XII has the higher average pass percentage.

Exercise 5D

1. Draw a histogram for the following data:

Ans-

-

5

8

16

18

13

0

2

4

6

8

10

12

14

16

18

20

No

. of

wo

rke

rs

Monthly Income

5000 5500 6000 6500 7000 7500

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling 3. Read the histogram and answer the following questions:

i). Use the graph to construct frequency distribution table. Ans-

Weights (in kg) Frequency

50 – 55 12

55 – 60 8

60 – 65 5

65 – 70 4

70 – 75 5

75 – 80 7

80 – 85 6

85 – 90 3

Total 50

ii). How many students weigh 70kg or more? Ans- (5+7+6+3) = 21 iii). How many students weigh less than 60kg? Ans- (12+8) = 20 iv). How many students are in the range 50 – 55 kg? Ans- 12 students. v). If one more student weighing 82kg joins this group, then how many students shall weigh 75kg or more? Ans- 17 students *Solve Q.2 and 4 by the same method.

Exercise 5E

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling Draw a pie chart for the given data. 1.

Ans-

Players Number Measure of central angle

Wicketkeeper cum batsman

2 (2/12) x 360°= 60°

Off spinner 2 (2/12) x 360°= 60°

Leg spinner 1 (1/12) x 360°= 30°

Specialist opening batsman 3 (3/12) x 360°= 90°

Batsman 4 (4/12) x 360°= 120°

Total 12 360°

Pie chart-

Players of the Indian Cricket Team

Wicketkeeper cum batsman

Off spinner

Leg spinner

Specialist opening batsman

Batsman

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling 2.

Ans-

Subject Marks Obtained Central Angle

English 105 (105/540) x360°=70°

Hindi 82.5 (82.5/540) x360°=55°

Mathematics 135 (135/540) x360°=90°

Social Science 97.5 (97.5/540) x360°=65°

Science 120 (120/540) x360°=80°

Total 540

Pie chart-

4.

Marks obtained by Nayantara

Engish

Hindi

Maths

Social Science

Science

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling

Ans-

Transport No. of office goers

Central Angle

Walk 10 (10/72) x 360°= 50°

Bus 12 (12/72) x 360°= 60°

Cycle 18 (18/72) x 360°= 90°

Train 24 (24/72) x 360°= 120°

Car 8 (8/72) x 360°= 40°

Total 72

Pie Chart-

Mode of transport

Walk

Bus

Cycle

Train

Car

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling 6.

Ans-

Expenditure heads Central Angle Expenditure

Wages 175° (175/360) x 900000 = Rs. 4,37,500

Rent 80° (80/360) x 900000 = Rs. 2,00,000

Maintenance 30° (30/360) x 900000 = Rs. 75,000

Electricity and water

25° (25/360) x 900000 = Rs. 62,500

Miscellaneous 50° (50/360) x 900000 = Rs. 1,25,000

Total 360°

*Solve Q. 3, 5 and 7 using the same method.

Exercise 5F 1. List the possible outcomes of the following experiments. i). Tossing a coin Ans- Heads(H), tails(T). ii). Throwing a dice. Ans- 1, 2, 3, 4, 5, 6. iii). Tossing two coins simultaneously. Ans- HH, HT, TH, TT iv). Spinning the wheel as shown in Figure 1.

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling

Ans- A, B, C, D, E. 2. When a dice is thrown, list the probability of an event of getting the following outcomes. i). A number greater than 4. Ans- P (A number greater than 4) = 2/6 = 1/3 ii). A composite number. P (A composite number) = 2/6 = 1/3 iii). A number not less than 3. P (A number not less than 3) = 4/6= 2/3

Ans- Total outcomes= 5+ 30 = 35 P(event)= No. of favourable outcomes/ No. of possible outcomes P (getting a prize)= 5/35 = 1/7

Ans- Total outcomes= 12 x 12 = 144 No. of defective pens= 12 No. of non-defective pens= 144-12= 132 P(event)= No. of favourable outcomes/ No. of possible outcomes i). P (defective pen) = 12/144 = 1/12 ii). P (non-defective pen) = 132/144 = 11/12

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling

Ans- No. of girls= 15 No. of boys= 10 Total students in the class= 15+10=25 P(event)= No. of favourable outcomes/ No. of possible outcomes i). P(girl) = 15/25 = 3/5 ii). P(boy) = 10/25 = 2/5 iii). P(pupil) = 25/25 = 1

Ans- P(event)= No. of favourable outcomes/ No. of possible outcomes i). No. of possible outcomes= 26 No. of favourable outcomes(vowel) = 5 P(Vowel)= 5/26 ii). possible outcomes – M, A, T, H, E, I, C, S No. of possible outcomes= 8 No. of favourable outcomes (vowels in the given word) = 3 P (vowel in the word MATHEMATICS) = 3/8

Ans- Total outcomes = 20 Not multiple of 3- 1,2, 4,5, 7,8,10,11,13,14,16,17,19,20 No.of favourable outcomes= 14 P(event)= No. of favourable outcomes/ No. of possible outcomes P (Not a multiple of 3) = 14/20 = 7/10

Lesson Notes

2021-2022 Subject-Mathematics Grade- VIII Chapter-5: Data Handling Ans- No. of possible outcomes = 52 P(event)= No. of favourable outcomes/ No. of possible outcomes i). No. of favourable outcomes = 13 P (a diamond) = 13/52 = ¼ ii). No. of favourable outcomes = 2 P (a red 7) = 2/52 = 1/26 iii). No. of favourable outcomes = 4 P (an ace) = 4/52 = 1/13

Ans- P(event)= No. of favourable outcomes/ No. of possible outcomes No. of possible outcomes = 8 +10= 18 No. of favourable outcomes= 8 P (red marble) = 8/18 = 4/9

Ans- P(event)= No. of favourable outcomes/ No. of possible outcomes No. of possible outcomes = 3+5+4= 12 i). No. of favourable outcomes= 4 P (blue ball) = 4/12 = 1/3 ii). No. of favourable outcomes= 3 P (White ball) = 3/12 = ¼ iii). No. of favourable outcomes=5 P (red ball) = 5/12 iv). No. of favourable outcomes= 5+4 = 9 P (not white ball) = 9/12 = ¾