CBSE Class 6 Mathematics Data Handling Worksheet Set 04

Question 1. The marks of a student in different subjects are given below:

Draw a bar graph from the above information.
Answer: To represent the given data on a bar graph, choose an appropriate scale on the vertical axis (y-axis), such as \(1 \text{ unit} = 10 \text{ marks}\). Plot the subjects on the horizontal axis (x-axis) and draw rectangular bars of uniform width with heights proportional to the marks obtained in each subject.
In simple words: Draw equally spaced bars for each subject where the height of each bar matches the marks scored.

Exam Tip: Always label both axes clearly and choose a consistent scale for the frequency axis.

Question 2. The following table shows the favourite sports of 250 students of a school.

Represent the data by a bar graph.
Answer: Take the horizontal axis to represent the sports and the vertical axis to represent the number of students. Choose a scale of \(1 \text{ unit} = 10 \text{ students}\). Draw bars of heights 90, 20, 60, 15, and 65 corresponding to Cricket, Football, Tennis, Badminton, and Swimming respectively.
In simple words: Represent each sport with a vertical bar whose height represents the number of students.

Exam Tip: Ensure equal spacing between consecutive bars to maintain visual accuracy.

Question 3. Given below is a table which shows the year wise strength of a school.

Represent this data by a bar graph.
Answer: Take the academic years along the x-axis and the number of students along the y-axis. Choose a scale of \(1 \text{ unit} = 200 \text{ students}\). Draw bars for each academic year with heights corresponding to 900, 950, 1200, 1400, and 1550.
In simple words: Plot the years on the horizontal line and student counts as vertical bars using a proper scale.

Exam Tip: When dealing with large numbers, choose a larger scale like 1 unit = 100 or 200 units to fit the graph neatly.

Question 4. The following table shows the number of motorcycles produced by a company during six consecutive years.

Draw a bar graph to represent this data.
Answer: Let the x-axis represent the years (2000 to 2005) and the y-axis represent the number of motorcycles. Use a scale of \(1 \text{ unit} = 2000 \text{ motorcycles}\) (with a kink on the y-axis if starting from 10,000, or starting from 0 with appropriate intervals). Draw bars with heights 12000, 13000, 13500, 14000, 15000, and 16000.
In simple words: Create vertical bars for each year representing the production numbers.

Exam Tip: Use a broken-scale symbol (kink) on the y-axis if the data starts at a large non-zero value like 12,000.

Question 5. The birth rate in five countries over a period of time is shown below:

Represent the data by a bar graph.
Answer: Represent the countries on the horizontal axis and the birth rate per thousand on the vertical axis. Choose a scale of \(1 \text{ unit} = 10 \text{ units of birth rate}\). Construct bars corresponding to heights of 52, 39, 28, 21, and 14 for China, India, UK, Nepal, and Singapore respectively.
In simple words: Draw bars showing the birth rate for each of the five countries.

Exam Tip: Label the y-axis clearly as "Birth rate per thousand".

Question 6. The population of six Indian states estimated in 2001 is as given below:

Represent the above data by a bar graph.
Answer: Place the states along the x-axis and population in lakhs along the y-axis. Choose a scale of \(1 \text{ unit} = 200 \text{ lakhs}\). Draw vertical bars of heights 820, 270, 210, 600, 1650, and 85 for the respective states.
In simple words: Represent the population of each state using vertical bars with a suitable scale.

Question 7. The following data shows India's total population from 1951 to 2001.

Represent the data by a bar graph.
Answer: Take the years on the horizontal axis and population (in millions) on the vertical axis. Choose a scale of \(1 \text{ unit} = 200 \text{ millions}\). Draw bars with heights corresponding to 360, 432, 540, 684, 852, and 1020.
In simple words: Draw a bar graph with years on the x-axis and population values on the y-axis.

Exam Tip: Keep the width of all bars uniform across the graph.

Question 8. The following table shows distances of some cities from Delhi.

Draw a bar graph to represent the above data.
Answer: Represent cities along the x-axis and distances (in km) along the y-axis. Choose a scale of \(1 \text{ unit} = 200 \text{ km}\). Draw bars with heights 1340, 1100, 1700, and 1220 for Kolkata, Mumbai, Chennai, and Hyderabad respectively.
In simple words: Plot the cities on the bottom axis and draw bars showing their distance from Delhi.

Exam Tip: Double-check the scale markings to ensure accurate plotting of intermediate values like 1340 and 1220.

Question 9. The following table shows the life expectancy average age to which people live in various countries in a particular year.

Represent the data by a bar graph.
Answer: Let the x-axis represent the countries and the y-axis represent life expectancy. Choose a scale of \(1 \text{ unit} = 10 \text{ years}\). Draw bars with heights 57, 70, 76, 43, and 36 for India, Britain, Japan, Ethiopia, and Cambodia respectively.
In simple words: Make a bar chart with countries at the bottom and life expectancy heights.

Exam Tip: Note that Ethiopia's printed value 433 in the source table is a typo for 43, which is used here for logical consistency.

Question 10. The data given below shows the average rainfall in Cheerapunji, from June to November of a certain year.

Draw a bar graph to represent this information.
Answer: Represent months along the x-axis and average rainfall along the y-axis. Choose a scale of \(1 \text{ unit} = 5 \text{ units of rainfall}\). Draw bars of heights 25, 30, 40, 20, 10, and 5 for June to November respectively.
In simple words: Draw bars showing monthly rainfall data.

Exam Tip: Ensure that the gaps between bars are equal across the graph.

Question 11. Gold Prices on five consecutive Mondays are as follows:

Draw a bar graph to represent this information.
Answer: Represent the Mondays on the x-axis and the rate per 10g (in Rs.) on the y-axis. Choose a scale of \(1 \text{ unit} = 1000 \text{ Rs.}\) (with a broken axis starting from 4000). Draw bars with heights 4850, 5100, 5250, 5500, and 6200.
In simple words: Create vertical bars for each Monday showing the gold price.

Exam Tip: Use a broken-axis symbol on the y-axis since the minimum value is 4850.

Question 12. The following table shows the average depth of some oceans and seas.

Draw a bar graph to represent them.
Answer: Let the x-axis represent the oceans and seas, and the y-axis represent the average depth in meters. Choose a scale of \(1 \text{ unit} = 500 \text{ m}\). Draw bars with heights 4000, 3950, 3900, 1350, and 1200 respectively.
In simple words: Plot the water bodies on the x-axis and their average depths as bar heights.

Exam Tip: Label the vertical axis clearly with "Average depth (in m)".

Question 13. Given below is a bar graph showing the heights of six mountain peaks.
Read the bar graph carefully and answer the following questions:

(i) What is the scale of this graph?
Answer: Looking at the vertical axis intervals, \(1 \text{ unit} = 1000 \text{ metres}\) (with major grid divisions every 1000m).
In simple words: The graph increases by 1000 meters for each unit on the vertical axis.

Exam Tip: Read the scale from the y-axis markings (0, 1000, 2000, ...).

Question 13(ii). Which is the highest peak and what is its height?
Answer: The highest peak is Everest (in Nepal) with a height of 8800 metres.
In simple words: Everest is the tallest peak shown, standing at 8800 meters.

Exam Tip: Identify the tallest bar on the graph to find the maximum value.

Question 13(iii). What is the ratio of the highest peak and next highest peak?
Answer:
Height of the highest peak (Everest) = 8800 m
Height of the next highest peak (K2 / Kanchenjunga) = 8600 m
Ratio = \(\frac{8800}{8600} = \frac{88}{86} = \frac{44}{43}\) or \(44:43\)
In simple words: Divide the height of the highest peak by the second highest peak and simplify the fraction.

Exam Tip: Always reduce ratios to their simplest form.

Question 13(iv). Arrange the heights of the given peaks in descending order.
Answer: 8800 m, 8600 m, 8600 m, 8100 m, 7800 m, 7750 m (Corresponding to Everest, K2, Kanchenjunga, Nanga Parbat, Nanda Devi, and Kamet).
In simple words: List the heights from the largest to the smallest value.

Exam Tip: Descending order means arranging numbers from highest to lowest.

1. Following is the choice of sweets of 30 students of Class VI.
Ladoo, Barfi, Ladoo, Jalebi, Ladoo, Rasgulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo,
Jalebi, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Ladoo,
Barfi, Rasgulla, Rasgulla, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo.
(a) Arrange the names of sweets in a table using tally marks.
(b) Which sweet is preferred by most of the students?

2. Total number of animals in five villages are as follows :
Village A : 80 Village B : 120
Village C : 90 Village D : 40
Village E : 60
Prepare a pictograph of these animals using one symbol to represent 10 animals and answer the following questions :
(a) How many symbols represent animals of village E?
(b) Which village has the maximum number of animals?
(c) Which village has more animals : village A or village C?

3. A survey of 120 school students was done to find which activity they prefer to do in their free time.
Preferred activity                 Number of students
Playing                                                 45
Reading story books                            30
Watching TV                                        20
Listening to music                               10
Painting                                               15
Draw a bar graph to illustrate the above data taking scale of 1 unit length = 5 students.
Which activity is preferred by most of the students other than playing?