Question:

A random survey of the number of children of various age groups playing in a park was found as follows:
Age (in years)
Number of children
1 − 2
5
2 − 3
3
3 − 5
6
5 − 7
12
7 − 10
9
10 − 15
10
15 − 17
4

Draw a histogram to represent the data above.

Age (in years)	Number of children
1 − 2	5
2 − 3	3
3 − 5	6
5 − 7	12
7 − 10	9
10 − 15	10
15 − 17	4

CBSE Class IX

Updated On: Nov 18, 2023

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Solution and Explanation

Here, it can be observed that the data has class intervals of varying width. The proportion of children per 1 year interval can be calculated as follows.

Age (In years)	Frequency (Number of children)	Width of classes	Length of rectangle
1 − 2	5	1	\(\frac{5 \times 1}{1}=5\)
2 − 3	3	1	\(\frac{3 \times 1}{1}=3\)
3 − 5	6	2	\(\frac{6 \times 1}{1}=6\)
5 − 7	12	2	\(\frac{12 \times 1}{1}=12\)
7 − 10	9	3	\(\frac{9 \times 1}{1}=9\)
10 − 15	10	5	\(\frac{10 \times 1}{1}=10\)
15 − 17	4	2	\(\frac{4 \times 1}{1}=4\)

Taking the age of children on x-axis and proportion of children per 1 year interval on yaxis, the histogram can be drawn as follows.
urvey of the number of children of various age groups playing in a park

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Section A	Section B
0 − 10	3	0 − 10	5
10 − 20	9	10 − 20	19
20 − 30	17	20 − 30	15
30 − 40	12	30 − 40	10
40 − 50	9	40 − 50	1

Section	Number of girls per thousand boys
Scheduled Caste (SC)	940
Scheduled Tribe (ST)	970
Non-SC/ST	920
Backward districts	950
Non-backward districts	920
Rural	930
Urban	910

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Number of letters	Number of surnames
1 − 4	6
4 − 6	30
6 − 8	44
8 − 12	16
12 − 20	4

Number of balls	Team A	Team B
1 − 6	2	5
7 − 12	1	6
13 − 18	8	2
19 − 24	9	10
25 − 30	4	5
31 − 36	5	6
37 − 42	6	3
43 − 48	10	4
49 − 54	6	8
55 − 60	2	10

Questions Asked in CBSE Class IX exam

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Concepts Used:

Statistics

Statistics is a field of mathematics concerned with the study of data collection, data analysis, data interpretation, data presentation, and data organization. Statistics is mainly used to acquire a better understanding of data and to focus on specific applications. Also, Statistics is the process of gathering, assessing, and summarising data in a mathematical form.

Mathematically there are two approaches for analyzing data in statistics that are widely used:

Descriptive Statistics -

Using measures of central tendency and measures of dispersion, the descriptive technique of statistics is utilized to describe the data collected and summarise the data and its attributes.

Inferential Statistics -

This statistical strategy is utilized to produce conclusions from data. Inferential statistics rely on statistical tests on samples to make inferences, and it does so by discovering variations between the two groups. The p-value is calculated and differentiated to the probability of chance() = 0.05. If the p-value is less than or equivalent to, the p-value is considered statistically significant.

Section A		Section B
Marks	Frequency	Marks	Frequency
0 − 10	3	0 − 10	5
10 − 20	9	10 − 20	19
20 − 30	17	20 − 30	15
30 − 40	12	30 − 40	10
40 − 50	9	40 − 50	1

A random survey of the number of children of various age groups playing in a park was found as follows:Age (in years) Number of children 1 − 2 52 − 333 − 56 5 − 7127 − 10910 − 151015 − 174Draw a histogram to represent the data above.