Class 8 Maths Notes for Data Handling

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CLASS 8
MATHS

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DATA HANDLING
Important Concepts:
In your day-to-day life, you might have come across information, such as:
(a) Runs made by a batsman in the last 10 test matches.
(b) Number of wickets taken by a bowler in the last 10 ODIs.
The information collected in all such cases is called data. Data is usually collected in
the context of a situation that we want to study
Usually, data available to us is in an unorganized form called raw data. To draw meaningful inferences, we
need to organize the data systematically either in ascending or descending order or in grouped form
Thus, the frequency distribution table for the above data can be written as

FREQUENCY OF DATA: Occurrence of a observation in the data is called frequency of the observation
Here 7 students have opted Art here 5 students opted Maths here

Grouping Data: We put the data in Grouped form by making a group of 2,3,5 … as depends on the
number of observations
ILLUSTRATION:
The following marks (out of 50) obtained in Mathematics by 60 students of Class VIII: 21, 10, 30, 22, 33, 5,
37, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 36, 18, 20, 38, 22, 44, 16, 24, 10, 27, 39, 28, 49,
29, 32, 23, 31, 21, 34, 22, 23, 36, 24, 36, 33, 47, 48, 50, 39, 20, 7, 16, 36, 45, 47, 30, 22, 17.

Note : Here in the above table in first class interval 0 – 10 there are number from 0 to 9 has occurred 2
times hen 2 is the frequency of the class 0 – 10
Limit of the Class Interval In the class interval 0 − 10 , 0 is called Lower limit and 10 is Upper limit
CLASS SIZE = UL - LL & CLASS MARK = (UL+LL)/2
Sometimes, data is represented graphically to give a clear idea of what it represents.
We have learnt different types of graphs in earlier classes: Pictograph, Bar graph
There are some more types of graphs like Histogram and Pie Chart
Histogram: A histogram is a diagram involving rectangles whose area is proportional to the frequency of a
variable and width is equal to the class interval.
Illustration: Dr Rao‘s Garden with 30 black cherry trees. Each tree is of a different height. The height of
the trees (in inches): 61, 63, 64, 66, 68, 69, 71, 71.5, 72, 72.5, 73, 73.5, 74, 74.5, 76, 76.2, 76.5, 77, 77.5, 78,
78.5, 79, 79.2, 80, 81, 82, 83, 84, 85, 87.

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PIE DIAGRAM:- The ―pie chart” is also known as a ―circle chart‖, dividing the circular statistical graphic
into sectors or sections to illustrate the numerical problems. Each sector denotes a proportionate part of the
whole.

This data is represented ias Pie chart or graph
Now to figure out how many degrees for each "pie slice" (correctly called a sector).
A Full Circle has 360 degrees, so we do this calculation:

CHANCE AND PROBABILITY: Sometimes it happens that during rainy season, you carry a raincoat
every day and it does not rain for many days. However, by chance, one day you forget to take the raincoat
and it rains heavily on that day.

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Suppose a coin is tossed at random. When we speak of a coin, we assume it to be ‗fair‘(as being ‗unbiased‘).
By the phrase ‗random toss‘, the coin can only land in one of two possible ways — either head up or tail up
We can reasonably assume that each outcome, head or tail, is as likely to occur as the other. We refer to this
by saying that the outcomes head and tail, are equally likely. Similarly for Dice
EVENT or OUTCOMES: Tossing a coin in an experiment and getting Head or Tail are OUTCOMES or
EVENT
𝑁( 𝐸) = 𝑁𝑜𝑠 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 and 𝑁(𝑆) = 𝑁𝑜𝑠 𝑜𝑓 𝑎𝑙𝑙 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑒𝑣𝑒𝑛𝑡𝑠
In a single toss of a coin 𝑆 = { 𝐻𝑒𝑎𝑑 , 𝑇𝑎𝑖𝑙 } , If you favor to come up head 𝐸 = { 𝐻𝑒𝑎𝑑 }
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔 𝒇𝒂𝒗𝒐𝒖𝒓𝒂𝒃𝒍𝒆 𝒕𝒐 𝑬
The probability of an event 𝑷(𝑬) is given as 𝑷 𝑬 = 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒂𝒍𝒍 𝒑𝒔𝒔𝒊𝒃𝒍𝒆 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔 𝒐𝒇 𝒕𝒉𝒆 𝒆𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕
0 ≤ 𝑃(𝐸) ≥ 0
Example: In a single throw of a dice find the probability of odd prime number.
Sol.𝑆 = {1,2,3,4,5,6} 𝑕𝑒𝑛𝑐𝑒 𝑁(𝑆) = 6 , 𝐸 = {3,5} 𝑕𝑒𝑛𝑐𝑒 𝑁(𝐸) = 2
𝑁 𝐸 2 1
Probability of odd prime numbers =P (Odd Prime) = 𝑁 𝑆 = 6 = 3
PROBLEMS ON DATA HANDLING
MCQ TYPE
1. The range of the data– 9, 8, 4, 3, 2, 1, 6, 4, 8, 10, 12, 15, 4, 3 is
(a) 15 (b) 14 (c) 12 (d) 10
2. The following data: 2, 5, 15, 25, 20, 12, 8, 7, 6, 16, 21, 17, 30, 32, 23, 40, 51, 15, 2, 9, 57, 19, 25 is
grouped in the classes 0 –5, 5 –10, 10 –15 etc. Find the frequency of the class 20 –25.
(a) 5 (b) 4 (c) 3 (d) 2
3. The pie chart depicts the information of viewers watching different type of channels on
TV. Which type of programmes are viewed the most?
(a) News (b) Sports (c) Informative (d). Entertainment
4. The central angle of the sectors in a pie chart will be a fraction of the angle
(a) 3600 (b) 1800 (c) 1000 (d) none of these

CASE STUDY BASED
5. In a city Delhi, there was a huge demand of opening new KVs
as big change in admission was reported. The admission
from the year 2003 to 2008 was shown by a graph on the basis of
the given graph answer the following.
(i) In which year 300 students were admitted?
(ii) In the year 2004-2005, How many students were admitted?
(iii) Name the type of Graph by which data is shown
SHORT ANSWER TYPE
6. In a single toss of a coin, find the probability of getting Tail.
7. What is the upper limit of the class interval 70 – 80?
8. What is the frequency of 15 in the data: 10,15,65,45,32,15,12,54 ?
LONG ANSWER TYPE
9. Draw the Pie chart for the given data
Favourite food North Indian South Indian Chinese Others
Number of people 30 40 25 25

10. Draw the double Bar graph for the following data
Expenditure per Month JANUARY FEBRUARY MARCH AUGUST SEPTEMBER
(Rs)
Family in Chandigarh 15000 18000 25000 27000 20000
Family in Delhi 8000 9000 9500 15000 13000
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11. 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, 8
. Using tally marks, make a frequency distribution table with class intervals 800 – 810, 810 – 820 and so
on.
SOLUTION:
Q1 C Q2 C Q3 D Q4 A Q5-i 2006-07

Q5-ii 200 Q5-iii Bar graph Q6 0.5 Q7 80 Q8 2

PRACTICE QUESTIONS
MCQ:
1 A dice is thrown two times and sum of the numbers appearing on the dice are noted. The number of
possible outcomes is
(a) 6 (b) 11 (c) 18 (d) 36
2 In a single throw of a dice what is the probability of getting 7?
(a) 6 (b) 1 (c) 0 (d) 3
3 In a bag, there are 4 Red balls and 6 Green balls. A ball is picked up at random, what is the
probability of getting a red ball?
(a) 0.6 (b) 1 (c) 0.5 (d) 0.4
4 What is the Lower limit of the class interval 30 - 40?
(a) 40 (b) 30 (c) 35 (d) 10
5 The correct statement about probability is
(a) P = 1 (b) P≥1 (c) 0 ≥ P ≤ 1 (d) 0 ≤ P ≤ 1
6 Sum of all central angle in the Pie chart is
(a) 3600 (b) 1800 (c) 1000 (d). None of these
7 Probability of rising the sun from east is
(a) 0.6 (b) 1 (c) 0.5 (d) 0.2
8 What does the height of rectangle shows in a Histogram?
(a) Upper limit (b) Lower limit (c) Frequency (d) Range
9 Today is Sunday, what is the chance of Monday tomorrow?
(a) 0.6 (b) 1 (c) 0.5 (d) 0.2
10 In a single toss of a coin what is the sum of probability of getting Head and Tail?
(a) 1 (b) 6 (c) 0 (d) 3
SHORT ANSWER TYPE
11. What does the height of a rectangle show in a histogram?
12. What do you say a geometric representation showing the relationship between a whole and its
parts?
13. What is the range of the data 30, 61, 55, 56, 60, 20, 26, 46, 28, 56 61
14. Write one example of a random experiment
15. What is the probability of choosing a vowel from the alphabets?
16. A double bar graph as given below shows the performance
of a student in two sessions.
Read the above graph, answer the following:
(a) What is the information given by the double bar graph?
(b) In which subject has the performance improved the
most?
(c) In which subject has the performance deteriorated?
(d) In which subject is the performance at par?
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(e) How many marks are scored by the student in science in both sessions?
LONG ANSWER TYPE
Q1. A glass jar contains 6 red, 5 green, 4 blue and some yellow marbles of same size. Ram takes out a
marble from the jar at random. If Probability of choosing blue ball is 0.2.
(a) What is the probability that the chosen marble is of Red colour?
(b) What is probability that the chosen marble is green colour?
Q2. Draw the Pie chart for the given information .
ACTIVITY TIME SPENT (Hrs)
Sleeping 4
School 8
Home work 6
Playing 4
Others 2
Q3. Draw the Bar Graph for the following data:
Village Nos Of Borewell (In Hundreds)
MAURANIPUR 4
KATERA 8
RAJGARH 6
SAFA 4
RAMPURA 2
Q.4 Draw the Histogram for the given data
Class interval 30-35 35-40 40-45 45-50 50-55 55-60
frequency 15 40 35 75 38 25
CASE STUDY BASED PROBLEMS
Q1. In a survey of a town of Uttar Pradesh, Hamirpur, 1800 males were
surveyed above the age of 20 the information collected was represented by a
Histogram as given below.
Reading the above graph answer the following
(a) How many males are literate for the Age groups 10 to 30 years?
(b) Which age group has maximum numbers of literate Males?
27. Government of India Planned a surveyed in a district of Madhya
Pradesh and the Given below is a pie chart showing the time spend by
a group of 350 children in different games. Observe it and answer the
questions that follows:
(A) How many children spend at least one hour in playing
games?
(B) How many children spend more than 2 hours in playing
games?
ANSWER

Q1 d Q6 a Q11 frequency Q16 41 Q21 0.3
Q2 c Q7 b Q12 Pie chart Q17 Mark Q22 0.25
compare
Q3 d Q8 c Q13 41 Q18 Eng
Q4 b Q9 b Q14 Toss a Q19 Hindi
coin
Q5 d Q10 b Q15 5/26 Q20 50,45

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TEST -1 DATA HANDLING (VIII) MM-20
All questions are compulsory
MCQ TYPE ( 1 Mark each)
1. In the class intervals 10 –20, 20 –30, 30-40 ,40 -50 etc., respectively, 20 lies in which class Intervals?
(a) 10 – 20 (b) 20 − 30 (c) 30 − 40 (d) 40 − 50
2. What is the probability of sun rising from west?
(a) 6 (b) 1 (c) 0 (d) 3
3. What sector angle will a sleep activity of 8 hrs in a day make at the centre?
(a) 1200 (b) 1800 (c) 1000 (d).3600
4. The Data available in an unorganised form is called
(a) Grouped (b)Primary (c) Raw (d) None
5. An experiment whose outcomes cannot be predicted exactly in advance is called a.
(a) Biased (b) sure (c) Random (d) None
SHORT ANSWER TYPE ( 1 Mark each )
6. A bag contains 6 Red balls 2 Green Balls 2 Green balls; a ball is picked up at random What is the
probability of getting a red ball?
7. Write the range for the data: 6, 8, 16, 22, 8, 20, 7, 25 ?
8. What scale on the A4 Graph Paper will you prefer to draw the bar graph for the given data?
Village A B C
Population 720 600 150
9. Write the sixth-class interval for a grouped data whose first two class intervals are 10 – 15 𝑎𝑛𝑑 15 – 20.
10. What is the class size for a given Class interval?
CASE STUDY BASED ( 05 Marks each)
11. The pie chart on the right shows the result of a survey carried out to find the modes
of travel used by the children to go to school.
Study the pie chart and answer the questions that follows:
(A) What is the most common mode of transport?
(B) What fraction of children travel by car?
(C) If 18 children travel by car, how many children took part in the survey?
(D) How many children use taxi to travel to school?
LONG ANSWER TYPE ( 5 Marks )
12. A dice is rolled once. What is the probability that the number on top will be
(a) Odd (b) Greater than 5 (c) A multiple of 3 (d) Less than 1

TEST -2 DATA HANDLING (VIII) MM-30
Q1. A group of 20 students recorded their heights (in cm). The data received were as given below. What is
the range?
150, 120, 112, 160, 155, 151, 158, 142, 148, 149, 161, 165, 140, 157, 156, 146, 148, 153, 138, 135. (2)
Q2. What is the probability of a number selected from the numbers 1, 2, 3, . . . . . , 20 such that it is a prime
number? (2)
Q3. A bag contains 3 blue and 2 red balls. A ball is drawn at random. What is the probability of drawing a
red ball? (2)
Q4. A die is thrown. What is the probability of getting: (4)
(i) an even number? (ii) an odd number? (iii) A number between 3 and 6? (iv) A prime number.
Q5. 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?
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(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. (4)
Q6. Draw a Bar Graph for the given data: (4)

Q7. Construct a pie chart for the given data: (4)

Q8. From a well shuffled deck of 52 playing cards, a card is selected at random. Find the probability of
getting
(i) a black card (ii) a black king (iii) an ace (iv) a card of diamond (4)
Q9. There are 1000 workers who travel from home to factory. (4)
The pie-graph shows the proportion of workers using various mode for traveling to work.
Study the pie-graph and answer the questions given below:
How many workers travel to factory
(i) by bus? (ii) by train? (iii) by cycle? (iv) on foot?

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