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Maths 4 Mark Question

Data Handling - II (Graphical Representation of Data as Histograms) · Maharashtra Board STD 8 (MSBSHSE - Semi English Medium). 2 questions.

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2 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
The following histogram shows the frequency distribution f the ages of 22 teachers in a school:
  1. What is the number of eldest and youngest teachers in the school?
  2. Which age group teachers are more in the school and which least?
  3. What is the size of the classes?
  4. What are the class marks of the classes?
Answer
  1. The eldest (50-55 years) = 1 person
This is because the height of the rectangle with class interval 50-55 as base is 1 unit.

The youngest (20-25 years) = 2 persons

This is because the height of the rectangle with class interval 20-25 as base is 2 units.
  1. The group containing the most number of teachers is 35-40 years. This is because the height of the rectangle with class interval 35-40 as base is the maximum.
The group containing the least number of teachers is 50-55 years. This is because the height of the rectangle with class interval 50-55 as base is the minimum.
  1. Class size = The range between the upper and the lower boundaries of the class.
For example, the size of the class 20-25 years is 5.
  1. $\text{Class mark}=\frac{\text{Upper limit }+\text{ Lower limit}}{2}$
For class 20-25:

$\text{Class mark}=\frac{20+25}{2}=\frac{45}{2}=22.5$

Similarly, the class marks of the other classes are 27.5, 32.5, 37.5, 42.5, 47.5, 52.5
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Question 24 Marks
The following histogram shows the monthly wages (in Rs.) of workers in a factory:
  1. In which wage-group the largest number of workers are being kept? What is their number?
  2. What wages are the least number of workers getting? What is the number of such workers?
  3. What is the total number of workers?
  4. What is the factory size?
Answer
  1. In the highest rectangle corresponds to the largest number of workers. The required interval is Rs. 950-1000. There are 8 workers in this interval.
  2. The lowest rectangle corresponds to the least number of workers. The required interval is Rs. 900-950. There are 2 workers in this interval.
  3. The total number of workers is the sum of workers in all the intervals. It can be calculated as follows:
  4. Total workers = 3 + 7 + 5 + 4 + 2 + 8 + 6 + 5 = 40 workers
  5. The factory intervals are 750-800, 800-850, ......, 1050-100. Hence, the factory size is 50.
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