CBSE Class 8 Mathematics Data Handling Assignment Set 11

VIII - Mathematics Assignment - 01 - Data Handling

Question 1. Following data represents the number of students in a school in various years. Draw a bar chart to represent the above information.

Answer:
To draw the bar chart, represent the years on the horizontal axis (X-axis) and the number of students on the vertical axis (Y-axis). Choose an appropriate scale on the Y-axis, such as 1 unit = 200 students.
1. Draw perpendicular axes intersecting at origin \(0\).
2. Mark 'Years' along the X-axis at equal intervals.
3. Mark 'Number of Students' along the Y-axis from 0 to 1600 with equal scale intervals of 200.
4. Construct rectangular bars of equal width for each year with heights corresponding to the respective number of students (e.g., height for 2006 is 600, 2007 is 1000, etc.).
In simple words: A bar chart uses rectangular bars to show comparisons among discrete categories of data.

Exam Tip: Always choose a uniform scale and maintain equal spacing between consecutive bars.

Question 2. The results of pass percentage of class X and XII in CBSE examination for 6 years are given below. Construct a double bar graph to represent the given data.

Answer:
To construct a double bar graph:
1. Take the years along the X-axis and pass percentage along the Y-axis.
2. Choose a suitable scale on the Y-axis, e.g., 1 unit = 10% (or 20% intervals).
3. For each year, draw two side-by-side bars representing Class X and Class XII using two distinct colors or shading patterns.
In simple words: A double bar graph compares two sets of related data across common categories side by side.

Exam Tip: Always include a legend indicating which bar color represents which category.

Question 3. The heights of 100 students of class IX of a school are given below.

Construct a bar graph to represent the above information. Read the graph and answer the following questions.
(a) What per cent of the students have their heights more than 160 cm?
(b) How many students have their heights less than 165 cm?
Answer:
(a)
Number of students with height more than 160 cm (i.e., heights 165 cm and 170 cm) = \(30 + 5 = 35\)
Total number of students = 100
Percentage = \(\frac{35}{100} \times 100\% = 35\%\)
(b)
Number of students with height less than 165 cm (i.e., heights 150 cm, 155 cm, and 160 cm) = \(5 + 20 + 40 = 65\)
In simple words: Add the frequencies of the required height groups and calculate percentage or total count accordingly.

Exam Tip: Read "more than" or "less than" conditions carefully to include or exclude boundary values correctly.

Question 4. Marks obtained by 100 students of a class out of 100 are given below. Construct a bar graph and answer the following questions.

(a) Students getting highest marks are entitled for a cash prize of Rs. 200. How much money is required for the distribution of prizes?
(b) Students obtaining marks below 33% are required to pay a fine of Rs. 20. Find total fine.
Answer:
(a)
Highest marks = 100
Number of students getting 100 marks = 5
Prize per student = Rs. 200
Total money required = \(5 \times \text{Rs. } 200 = \text{Rs. } 1000\)
(b)
Marks below 33% (out of 100 marks total) means marks less than 33.
The mark categories below 33 are 10, 15, 18, and 25.
Number of students in these categories = \(10 + 30 + 22 + 15 = 77\)
Fine per student = Rs. 20
Total fine = \(77 \times \text{Rs. } 20 = \text{Rs. } 1540\)
In simple words: Multiply the number of eligible students by the respective amount (prize or fine) to get the total sum.

Exam Tip: Double-check the threshold marks (like 33% out of 100) before summing up the student frequencies.

Question 5. Read the above bar graph and answer the following questions.
(a) What information the above bar graph represent?
(b) In which year the export is minimum?
(c) Is the growth of export uniform?
(d) In 2010 what is the export?
(e) In which year the export is maximum?
Answer:
(a) It represents export in various years.
(b) 2006 (Export = 3 Crores)
(c) No (Exports fluctuate between increasing and decreasing values across the years)
(d) 5 Crores Rupees
(e) 2009 (Export = 8 Crores)
In simple words: Read values directly by looking at the height of each bar corresponding to the Y-axis scale.

Exam Tip: Always verify units (e.g., Crores of Rupees) given on the Y-axis label when writing numerical answers.