The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian Society is given below: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
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.
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 |
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.
Solution and Explanation
(i) We represent the given information in the form of a bar graph. We construct the bar diagram through the following steps:
Step 1. Draw two perpendicular axes OX and OY on a plane paper.
Step 2. Along OX mark “Section” and along OY mark “Number of girls per thousand boys”.
Step 3. Along OX choose suitable width for each bar.
Step 4. Along OY choose an appropriate scale. Here choose 1 large division = 100 girls
Step 5. Calculate the heights of the various bars as follows:
(a) Height of bar for Scheduled caste =\(\frac{1}{100}\) x 940 = 9.4 large divisions
(b) Height of bar for Scheduled tribe =\(\frac{1}{100}\) x 970 = 9.7 large divisions
(c) Height of bar for Non SC / ST = \(\frac{1}{100}\) x 920 = 9.2 large divisions
(d) Height of bar for Backward districts = \(\frac{1}{100}\) x 950 = 9.5 large divisions
(e) Height of bar for non-backward districts = \(\frac{1}{100}\) x 920 = 9.2 large divisions
(f) Height of bar for Rural = \(\frac{1}{100}\) x 930 = 9.3 large divisions
(g) Height of bar for Urban =\(\frac{1}{100}\) x 910 = 9.1 large divisions
(ii) From the graph we observe that in each section the number of girls are nearly same. We also observe that the number of girls in each section are less than the boys. Also, it is observed that the number of girls to the nearest ten per thousand boys are maximum in scheduled tribes whereas they are minimum in urban areas.
Top Questions on Graphical Representation of Data
- The following table gives the distribution of students of two sections according to the marks obtained by him:
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
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.- CBSE Class IX
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- The following table gives the lifetimes of 400 neon lamps:
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
(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a lifetime of more than 700 hours?- CBSE Class IX
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- 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
Number of letters
Number of surnames
1 − 4
6
4 − 6
30
6 − 8
44
8 − 12
16
12 − 20
4
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.- CBSE Class IX
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- 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.- CBSE Class IX
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- Graphical Representation of Data
- The runs scored by the two teams A and B in the first 60 balls in a cricket match are given below:
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
Represent the data of both the teams on the same graph by frequency polygons.
[Hint: First make the class intervals continuous.]- CBSE Class IX
- Mathematics
- Graphical Representation of Data
Questions Asked in CBSE Class IX exam
- Explain what the reasons for the following are.
(i) Einstein leaving the school in Munich for good.
(ii) Einstein wanting to study in Switzerland rather than in Munich.
(iii) Einstein seeing in Mileva an ally.
(iv) What do these tell you about Einstein?- CBSE Class IX
- A truly beautiful mind
- (i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)- CBSE Class IX
- The snake and the mirror
In Fig. 9.26, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.
- CBSE Class IX
- Angle Subtended by an Arc of a Circle
- Name the two temples the author visited in Kathmandu.
- CBSE Class IX
- Kathmandu
Look up the dictionary entries for the words sympathy, familiarity, comfort, care, and surprise. Use the information given in the dictionary and complete the table.
Noun, Adjective, Adverb, Verb, Meaning:
sympathy
familiarity
comfort
care
surprise- CBSE Class IX
- If I were you
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.