CBSE Class 8 Mathematics Data Handling Assignment Set 09

VIII - Mathematics Assignment No - 03 - Data Handling

Question 1. Below is the histogram showing the marks obtained by 45 students of a class. Look at the above histogram and answer the following questions.
(a) What is the class size?
Answer: Upper limit - Lower limit = 10 - 0 = 10
In simple words: The width of each class interval in the histogram is 10.

Exam Tip: Class size is found by subtracting the lower limit from the upper limit of any continuous class interval.

Question 1.(b) How many students obtained less than 20 marks?
Answer: Number of students in interval 0-10 = 2
Number of students in interval 10-20 = 6
Total students obtaining less than 20 marks = 2 + 6 = 8
In simple words: Add the frequencies of the first two bars (0-10 and 10-20).

Exam Tip: "Less than 20" includes all intervals starting from 0 up to 20.

Question 1.(c) How many students obtained 30 or more marks but less than 50?
Answer: Number of students in interval 30-40 = 3
Number of students in interval 40-50 = 8
Total students = 3 + 8 = 11
In simple words: Combine the student counts for the intervals 30-40 and 40-50.

Exam Tip: Look carefully at the vertical axis height corresponding to each bar between 30 and 50.

Question 1.(d) What is the interval of highest marks and how many students are there in this interval?
Answer: The interval with the highest frequency (tallest bar) is 20-30.
Number of students in this interval = 10
In simple words: The tallest bar represents 10 students in the 20-30 marks range.

Exam Tip: Identify the maximum frequency from the Y-axis and trace it back to the corresponding X-axis interval.

Question 2. Draw the histogram for the following table representing the weights of different teachers.

Answer: 1. Take weight along the X-axis on a suitable scale (e.g., 1 cm = 5 kg) and start with a kink (broken axis symbol) from 0 to 45 since data starts at 45.
2. Take the number of teachers along the Y-axis on a suitable scale (e.g., 1 cm = 2 teachers).
3. Draw adjacent rectangular bars for each weight interval with heights proportional to the number of teachers.
In simple words: A histogram is constructed by drawing connected bars where the area of each bar corresponds to the frequency of teachers in that weight range.

Exam Tip: Always use a broken axis symbol on the X-axis if the scale does not start from zero.

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

Answer: 1. Represent Monthly Salary along the X-axis and No. of persons along the Y-axis.
2. Use a broken axis on the X-axis between 0 and 1000.
3. Draw continuous rectangular bars for each salary bracket representing the given frequencies.
In simple words: Plot salary ranges on the horizontal axis and frequencies on the vertical axis to create a continuous bar graph.

Exam Tip: Ensure all bars touch each other since class intervals are continuous.

Question 4. Look at the above histogram showing the ages of different teachers.
(i) In what age group maximum no. of teachers are there and what is their number?
Answer: Age group 35-40 years has the maximum number of teachers, and their number is 11.
In simple words: The tallest bar is in the 35-40 range with a height of 11.

Exam Tip: Identify the highest bar first to locate the maximum frequency category.

Question 4.(ii) What is the no. of teachers having their ages 25 yrs or more but less than 45 yrs?
Answer: Teachers in 25-30 = 4
Teachers in 30-35 = 8
Teachers in 35-40 = 11
Teachers in 40-45 = 9
Total number of teachers = 4 + 8 + 11 + 9 = 32
In simple words: Sum the frequencies of all four bars from age 25 to 45.

Exam Tip: Include all intervals starting from 25 up to the lower boundary of 45.

Question 4.(iii) How many teachers are of the age 40 years or more?
Answer: Teachers in 40-45 = 9
Teachers in 45-50 = 5
Total teachers = 9 + 5 = 14
In simple words: Add the frequencies of the last two intervals (40-45 and 45-50).

Exam Tip: "40 years or more" means all intervals starting from 40 onwards.

Question 4.(iv) Find class size of every class.
Answer: Class size = Upper limit - Lower limit = 30 - 25 = 5 (for all classes)
In simple words: The width of every age group interval is 5 years.

Question 4.(v) How many teachers are there in the age group 35-40?
Answer: Number of teachers in the age group 35-40 is 11.
In simple words: Read the height of the bar corresponding to the 35-40 interval.

Exam Tip: Look directly at the frequency corresponding to the interval 35-40 on the Y-axis.