Data Handling - Class 8 - Mathematics
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Examples - Data Handling | NCERT | Mathematics | Class 8
Adjoining pie chart (Fig 4.4) gives the expenditure (in percentage) on various items and savings of a family during a month.
(i) On which item, the expenditure was maximum?
(ii) Expenditure on which item is equal to the total savings of the family?
(iii) If the monthly savings of the family is ⟨₹⟩ 3000, what is the monthly expenditure on clothes?
(i) The expenditure on Food is the maximum with 25%.
(ii) The expenditure that is equal to the total savings (15%) of the family is on Education for children and Savings itself.
(iii) To find the monthly expenditure on clothes given the saving is ₹3000, we first determine the total monthly income. Since savings constitute 15% of the total income, we calculate the total income using the formula for percentage:
$$ Income = \frac{Savings}{Percentage} = \frac{3000}{0.15} $$
Next, we use the percentage for clothes expenditure $10%$ to find the monthly expenditure on clothes:
$$ Expenditure:on:clothes = Income \times Percentage:on:clothes $$
Let's calculate these to get the exact value. The calculations yield the following results:
The total monthly income of the family is ₹20,000.
The monthly expenditure on clothes is ₹2,000.
On a particular day, the sales (in rupees) of different items of a baker's shop are given below.
Item | Quantity |
---|---|
Ordinary bread | 320 |
Fruit bread | 80 |
Cakes and pastries | 160 |
Biscuits | 120 |
Others | 40 |
Total | 720 |
Draw a pie chart for this data.
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Sign up nowA bag has 4 red balls and 2 yellow balls. (The balls are identical in all respects other than colour). A ball is drawn from the bag without looking into the bag. What is the probability of getting a red ball? Is it more or less than getting a yellow ball?
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Sign up nowExercise 4.2 - Data Handling | NCERT | Mathematics | Class 8
List the outcomes you can see in these experiments.
(a) Spinning a wheel
A wheel with five segments labelled A, A, B, C, D
(b) Tossing two coins together
Experiment a: Spinning a Wheel
For a wheel with five segments labelled A, A, B, C, D, the possible outcomes based on the segments the spinner can land on are:
A
B
C
D
Note: Here, 'A' appears twice, but since the outcome is based on the label it lands on, we consider each label as a unique outcome despite the frequency of labels on the wheel.
Experiment b: Tossing Two Coins Together
When tossing two coins together, each coin has two possible outcomes: Heads (H) or Tails (T). Thus, the possible combined outcomes for tossing two coins together are:
Heads, Heads (HH)
Heads, Tails (HT)
Tails, Heads (TH)
Tails, Tails (TT)
Here, the order is considered (i.e., HT is different from TH) because it indicates which coin shows what side.
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.
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Sign up nowFind 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. 4 red apples and 3 green apples.
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Sign up nowNumbers 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?
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Sign up nowIf 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?
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Sign up nowFind the probabilities of the events given in Q 2
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Sign up nowExercise 4.1 - Data Handling | NCERT | Mathematics | Class 8
A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining table shows the findings of this survey. From this table 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?
Music Type | Percentage |
---|---|
Classical | 10% |
Semi Classical | 20% |
Folk | 30% |
Light | 40% |
(i) Total Number of Surveyed Young People
Given that 20 people liked classical music and it represents 10% of the total surveyed population, we can calculate the total number of surveyed young people using the proportion:
$$ \begin{align*} \frac{20}{x} &= \frac{10}{100} \ x &= \frac{20 \times 100}{10} \ x &= 200 \end{align*} $$
So, 200 young people were surveyed.
(ii) Type of Music Liked by the Maximum Number of People
From the given percentages, we can see Light music has the highest percentage, 40%. This means Light music is liked by the maximum number of people.
(iii) Number of CDs of Each Type
If a cassette company were to make 1000 CDs, the number of each type they would make can be calculated based on the percentages for each music type:
Classical Music: $1000 \times 10% = 100$
Semi Classical Music: $1000 \times 20% = 200$
Folk Music: $1000 \times 30% = 300$
Light Music: $1000 \times 40% = 400$
Therefore, they would make 100 CDs of Classical music, 200 CDs of Semi Classical music, 300 CDs of Folk music, and 400 CDs of Light music.
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.
Season | No. of votes |
---|---|
Summer | 90 |
Rainy | 120 |
Winter | 150 |
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Sign up nowDraw a pie chart showing the following information. The table shows the colours preferred by a group of people.
Colours | Number of people |
---|---|
Blue | 18 |
Green | 9 |
Red | 6 |
Yellow | 3 |
Total | 36 |
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Sign up nowThe 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).
Subject | Angle |
---|---|
Mathematics | 90° |
Science | 65° |
Social Science | 80° |
English | 55° |
Hindi | 70° |
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Sign up nowThe number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.
Language | Hindi | English | Marathi | Tamil | Bengali | Total |
---|---|---|---|---|---|---|
Number | 40 | 12 | 9 | 7 | 4 | 72 |
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