CBSE Class 8 Mathematics Data Handling Assignment Set 07

Mathematics Assignment No. 5 - Data Handling

Question 1. Following data represent the expenditure on food items

Represent the above data in the form of pie chart.
Answer: Total expenditure = \(720 + 360 + 540 + 900 = 2520\)
Central angle for each item = \(\left(\frac{\text{Component Expenditure}}{\text{Total Expenditure}}\right) \times 360^\circ\)
Food = \(\frac{720}{2520} \times 360^\circ = 102.86^\circ\)
Cloth = \(\frac{360}{2520} \times 360^\circ = 51.43^\circ\)
Rent = \(\frac{540}{2520} \times 360^\circ = 77.14^\circ\)
Education = \(\frac{900}{2520} \times 360^\circ = 128.57^\circ\)
In simple words: To draw a pie chart, calculate the central angle for each category by dividing its value by the total sum and multiplying by \(360^\circ\).

Exam Tip: Always verify that the sum of all central angles equals \(360^\circ\) before drawing the pie chart.

Question 2. The no. of Students enrolled in various Subjects are as follows.

Represent the above data in the form of Pie chart.
Answer: Total students = \(50 + 80 + 16 + 14 + 20 = 180\)
Central angle = \(\left(\frac{\text{Number of students in a subject}}{\text{Total students}}\right) \times 360^\circ\)
English = \(\frac{50}{180} \times 360^\circ = 100^\circ\)
Hindi = \(\frac{80}{180} \times 360^\circ = 160^\circ\)
Maths = \(\frac{16}{180} \times 360^\circ = 32^\circ\)
Science = \(\frac{14}{180} \times 360^\circ = 28^\circ\)
Social Studies = \(\frac{20}{180} \times 360^\circ = 40^\circ\)
In simple words: Find the fraction of students in each subject out of the total, then multiply by \(360^\circ\) to find the angle.

Exam Tip: Check your calculations by adding all central angles: \(100^\circ + 160^\circ + 32^\circ + 28^\circ + 40^\circ = 360^\circ\).

Question 3. A student spends different hours of a working day as follows. Represent the information in the form of pie chart.

Answer: Total hours in a day = \(8 + 3 + 2 + 8 + 3 = 24\)
Central angle = \(\left(\frac{\text{Hours for activity}}{\text{Total hours}}\right) \times 360^\circ\)
School = \(\frac{8}{24} \times 360^\circ = 120^\circ\)
Homework = \(\frac{3}{24} \times 360^\circ = 45^\circ\)
Playing = \(\frac{2}{24} \times 360^\circ = 30^\circ\)
Sleeping = \(\frac{8}{24} \times 360^\circ = 120^\circ\)
Misc = \(\frac{3}{24} \times 360^\circ = 45^\circ\)
In simple words: Divide the number of hours spent on each activity by 24 and multiply by \(360^\circ\) to get the corresponding angle.

Exam Tip: A full day has 24 hours, so the denominator for all calculations will always be 24.

Question 4. The adjoining Pie chart represents a survey of different types of music. Answer the following questions from the pie chart.
(i) If 20 people liked semi-classical music, how many young people were surveyed?
(ii) Which type of music is liked by the maximum no. of people?
(iii) If a Cassette Company were to make 1000 CDs, how many of each type would they make?
Answer:
(i) Let total people surveyed be \(x\).
Given that \(20\%\) of total people = 20
\(\frac{20}{100} \times x = 20\)
\(x = \frac{20 \times 100}{20} = 100\)
Total people surveyed = 100.

(ii) Light music is liked by the maximum number of people (\(40\%\)).

(iii) Number of CDs for each type out of 1000:
Light music = \(\frac{40}{100} \times 1000 = 400\)
Folk music = \(\frac{30}{100} \times 1000 = 300\)
Semi-classical music = \(\frac{20}{100} \times 1000 = 200\)
Classical music = \(\frac{10}{100} \times 1000 = 100\)
In simple words: Use percentages from the pie chart to find total values or specific shares by applying direct proportions.

Exam Tip: Always convert percentages to fractions or decimals when calculating actual numbers from a total.

Question 5. The adjoining pie chart represents number of 720 Students of class VII to X of a school. By studying the pie chart, answer the following questions.
(i) How many students are in class X?
(ii) How many students are more in class VII than in class VIII?
(iii) Find the ratio of the students of class IX to that of class X.
Answer:
Total students = 720
(i) Students in class X (angle = \(60^\circ\)):
\(\frac{60^\circ}{360^\circ} \times 720 = \frac{1}{6} \times 720 = 120\)

(ii) Difference in angle between class VII (\(120^\circ\)) and class VIII (\(105^\circ\)):
\(120^\circ - 105^\circ = 15^\circ\)
Number of more students = \(\frac{15^\circ}{360^\circ} \times 720 = \frac{1}{24} \times 720 = 30\)

(iii) Ratio of students of class IX (\(75^\circ\)) to class X (\(60^\circ\)):
\(\frac{75^\circ}{60^\circ} = \frac{75}{60} = \frac{5}{4} = 5:4\)
In simple words: Use the central angle fraction multiplied by the total population to find student counts, or directly compare angles for ratios and differences.

Exam Tip: For ratios of categories from the same pie chart, you can directly compare their central angles without converting to actual student numbers first.