CBSE Class 8 Mathematics Data Handling Assignment Set 05

Data Handling

Question 1. The marks obtained by 40 students of a class in an examination is given below .Prepare a frequency distribution table taking one of the class interval as 10 - 15.
23, 2, 10, 20, 12, 9, 7, 0, 5, 3, 5, 16, 8, 5, 12, 18, 8, 12, 6, 16, 17, 18, 3, 23, 7, 13, 18, 10, 21, 13, 1, 7, 15, 13, 21, 24, 19, 16, 2, 23
Answer: To prepare a frequency distribution table with a class interval size of 5 (since 15 - 10 = 5), we set up the class intervals starting from 0 up to 25 and use tally marks to count the frequency of each observation.
Total number of students = 40

In simple words: We group the marks into ranges of 5 and count how many students fall into each group using tally marks.

Exam Tip: Always verify that the sum of all frequencies equals the total given number of observations (40 in this case) to ensure no data point was missed.

Question 2. Draw the histogram of the following table showing the weights of different students.

Answer: To draw a histogram, represent the weights (class intervals) along the horizontal axis (X-axis) and the number of students (frequencies) along the vertical axis (Y-axis). Since the intervals are continuous and start from 45, a kink mark (jagged line) is used on the X-axis between 0 and 45.
In simple words: A histogram is a bar graph with no spaces between the bars, where the height of each bar represents the frequency of that weight interval.

Exam Tip: Remember to draw adjacent bars with zero gap since class intervals are continuous, and mark the break on the X-axis if the scale does not start from zero.

Question 3. Prepare a histogram of the following table showing the monthly salary of different persons.

Answer: To construct the histogram for monthly salary:
1. Take monthly salary along the X-axis and number of persons along the Y-axis.
2. Include a kink mark (break symbol) on the X-axis between 0 and 1000 since the data starts directly from 1000.
3. Draw adjacent rectangular bars for each class interval with heights proportional to the given frequencies.
In simple words: Plot the salary ranges on the bottom axis and draw touching bars whose heights match the number of persons in each salary bracket.

Exam Tip: Label both axes clearly with units (e.g., Monthly salary in Rs, No of persons) to secure full marks.

Question 4. The following data represent the expenditure on food items. Represent the data using a Pie - Chart

Answer: First, calculate the total expenditure and the central angle for each item using the formula:
\(\text{Central Angle} = \left( \frac{\text{Value of Item}}{\text{Total Value}} \right) \times 360^{\circ}\)
Total Expenditure = \(720 + 360 + 540 + 900 = 2520\)

1. Food: \(\left( \frac{720}{2520} \right) \times 360^{\circ} = \left( \frac{2}{7} \right) \times 360^{\circ} = 102.86^{\circ}\)
2. Clothes: \(\left( \frac{360}{2520} \right) \times 360^{\circ} = \left( \frac{1}{7} \right) \times 360^{\circ} = 51.43^{\circ}\)
3. Rent: \(\left( \frac{540}{2520} \right) \times 360^{\circ} = \left( \frac{3}{14} \right) \times 360^{\circ} = 77.14^{\circ}\)
4. Education: \(\left( \frac{900}{2520} \right) \times 360^{\circ} = \left( \frac{5}{14} \right) \times 360^{\circ} = 128.57^{\circ}\)

In simple words: Find the fraction of the total amount spent on each category, multiply by 360 degrees to get the angle, and draw those slices in a circle.

Exam Tip: Always double check that the sum of all calculated central angles equals exactly \(360^{\circ}\).

Question 5. The number of students enrolled in various subjects are given below. Prepare a Pie - Chart to represent the data.

Answer: Calculate the total number of students and the central angle for each subject:
Total Students = \(50 + 80 + 16 + 14 + 20 = 180\)
Formula: \(\text{Central Angle} = \left( \frac{\text{No. of students in subject}}{\text{Total students}} \right) \times 360^{\circ}\)

1. English: \(\left( \frac{50}{180} \right) \times 360^{\circ} = 50 \times 2^{\circ} = 100^{\circ}\)
2. Hindi: \(\left( \frac{80}{180} \right) \times 360^{\circ} = 80 \times 2^{\circ} = 160^{\circ}\)
3. Maths: \(\left( \frac{16}{180} \right) \times 360^{\circ} = 16 \times 2^{\circ} = 32^{\circ}\)
4. Science: \(\left( \frac{14}{180} \right) \times 360^{\circ} = 14 \times 2^{\circ} = 28^{\circ}\)
5. S.Science: \(\left( \frac{20}{180} \right) \times 360^{\circ} = 20 \times 2^{\circ} = 40^{\circ}\)

In simple words: Divide each subject's student count by the total number of students (180), then multiply by 360 degrees to get the exact slice size for the pie chart.

Exam Tip: Verify your angle calculations by checking that \(100^{\circ} + 160^{\circ} + 32^{\circ} + 28^{\circ} + 40^{\circ} = 360^{\circ}\).