A random survey of the number of children of various age groups playing in a park was found as follows:
Draw a histogram to represent the data above.
Solution:
- From the given data, we can observe that the class intervals have varying widths. This will make the rectangular bars have varying widths and will give us a misleading picture of the data.
- The areas of the rectangles should be proportional to the frequencies in a histogram.
- So, we need to make certain modifications in the lengths so that area is proportional to the frequencies.
- The lengths of the rectangles are then modified to be proportionate to the class size
- For instance, when the class size is 5, the length of the rectangle is 10. So when the class size is 1, the length of the rectangle will be 10/5 × 1 = 2
We will proceed in similar manner, to get the following table:
Age (in years) |
Number of children |
Width of the Class |
Length of the rectangle |
1–2 |
5 |
1 |
(5 × 1)/1 = 5 |
2–3 |
3 |
1 |
(3 × 1)/1 = 3 |
3–5 |
6 |
2 |
(6 × 1)/2 = 3 |
5–7 |
12 |
2 |
(12 × 1)/2 = 6 |
7–10 |
9 |
3 |
(9 × 1)/3 = 3 |
10–15 |
10 |
5 |
(10 × 1)/5 = 2 |
15–17 |
4 |
2 |
(4 × 1)/2 = 2 |
Taking the age of children on x-axis and the proportion of children per year on y-axis, the histogram will be:
☛ Check: NCERT Solutions Class 9 Maths Chapter 14
Video Solution:
A random survey of the number of children of various age groups playing in a park was found as follows: Draw a histogram to represent the data above.
NCERT Solutions for Class 9 Maths Chapter 14 Exercise 14.3 Question 8
Summary:
The data of a random survey of the number of children of various age groups playing in a park is given. We have made a Histogram to represent the data.
☛ Related Questions:
- The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous] ii) Is there any other suitable graphical representation for the same data? iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
- The following table gives the lifetimes of 400 neon lamps: (i) Represent the given information with the help of a histogram. (ii) How many lamps have a life time of more than 700 hours?
- The following table gives the distribution of students of two sections according to the marks obtained by them: Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
- The runs scored by two teams A and B on the first 60 balls in a cricket match are given below: Represent the data of both the teams on the same graph by frequency polygons. [Hint: First make the class intervals continuous.]
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