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 |
Draw a histogram to represent the data above.
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. 
Top Questions on Graphical Representation of Data
- A survey conducted by an organization for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):
S.No. Causes Female fatality rate (%) 1. Reproductive health conditions 31.8
2. Neuropsychiatric conditions 25.4
3. Injuries 12.4
4. Cardiovascular conditions 4.3
5. Respiratory conditions 4.1
6. Other causes 22.0
(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women’s ill health and death worldwide?
(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.- CBSE Class IX
- Mathematics
- Graphical Representation of Data
- 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
- Mathematics
- 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
- Mathematics
- Graphical Representation of Data
- 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.- CBSE Class IX
- Mathematics
- Graphical Representation of Data
- 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
- Mathematics
- Graphical Representation of Data
Questions Asked in CBSE Class IX exam
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
(viii) I finished my work ________ so that I could go out to play
- CBSE Class IX
- The fun they had
- Is there any difference between the two roads as the poet describes them:
(i) in stanzas two and three?
(ii) in the last two lines of the poem?- CBSE Class IX
- The fun they had
- Here is your diary entry when you visited Agra. Read the points and try to write a travelogue describing your visit to Agra and the Taj Mahal. You may add more details.
January 2003 — rise before dawn — take the Shatabdi Express at 6.15 a.m. from Delhi — meet a newly-married couple on train — talk about Himachal Pradesh — get off the train — enter the once-grand city, Agra — twisted alleys — traffic dense — rickshaws, cars, people — vendors selling religious artifacts, plastic toys, spices and sweets — go to the Taj Mahal — constructed entirely of white marble — magical quality — colour changes with varying of light and shadow — marble with gemstones inside — reflection of the Taj Mahal in the pond — school-children, tourists — tourist guides following people.- CBSE Class IX
- Kathmandu
- 1.The (site, cite) of the accident was (ghastly/ghostly).
2. Our college (principle/principal) is very strict.
3. I studied (continuously/continually) for eight hours.
4. The fog had an adverse (affect/effect) on the traffic.
5. Cezanne, the famous French painter, was a brilliant (artist/artiste).
6. The book that you gave me yesterday is an extraordinary (collage/college) of science fiction and mystery. 7. Our school will (host/hoist) an exhibition on cruelty to animals and wildlife conservation.
8. Screw the lid tightly onto the top of the bottle and (shake/shape) well before using the contents.- CBSE Class IX
- If I were you
- Discuss what these phrases mean to you.
(i) a yellow wood
(ii) it was grassy and wanted wear
(iii) the passing there
(iv) leaves no step had trodden black
(v) how way leads on to way- CBSE Class IX
- The fun they had
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.