CBSE Class 6 Mathematics Data Handling Worksheet Set 03

Question 1. In a bar graph, the space between the two bars is kept
(a) Different
(b) uniform
(c) none of the options.
Answer: (b) uniform
In a bar graph, bars are drawn with equal spacing between them to maintain visual clarity and proper comparison.
In simple words: The gaps between bars in a bar graph are always equal.
Exam Tip: Remember that uniform spacing and equal width of bars are two fundamental rules of drawing bar graphs.

Question 2. In a bar graph the bars are of equal
(a) Width
(b) height
(c) none of the options.
Answer: (a) Width
All bars in a standard bar graph must have the same width, while their heights represent the respective numerical values.
In simple words: Every bar in a bar graph has the exact same thickness or width.

Exam Tip: Do not confuse bar width with bar height; height changes according to the data value, but width remains constant.

Question 3. The heights (in cm) of students of a class were recorded as below: 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125 (unsorted source data: 116, 117, 125, 116, 118, 120, 125, 121, 124, 117, 116, 115, 119, 121, 124, 117, 116, 119, 123, 120, 116, 121, 119, 116, 118, 125, 116, 119, 123, 122, 121, 120). Arrange the data in a tabular form using tally marks.
Answer:
First, count the frequency of each height from the given data values and represent them using tally marks:
- Height 115: 1 time
- Height 116: 9 times
- Height 117: 3 times
- Height 118: 2 times
- Height 119: 4 times
- Height 120: 3 times
- Height 121: 4 times
- Height 122: 1 time
- Height 123: 2 times
- Height 124: 2 times
- Height 125: 3 times
Total frequency = 1 + 9 + 3 + 2 + 4 + 3 + 4 + 1 + 2 + 2 + 3 = 32 students.
 

In simple words: We count how many times each height appears and group them in bundles of five tally marks.
Exam Tip: Always cross out numbers from the raw data as you count them to avoid missing any values or double-counting.

Question 4. The weights of 20 marbles (in grams) are given below 32, 34, 31, 28, 32, 27, 29, 31, 28, 32, 25, 27, 28, 32, 34, 28, 29, 31, 28, 25. Draw a pictograph using 1 circle = 1 marble.
Answer:
First, prepare the frequency table for marble weights:
- 25 g: 2 marbles
- 27 g: 2 marbles
- 28 g: 6 marbles
- 29 g: 2 marbles
- 31 g: 3 marbles
- 32 g: 4 marbles
- 34 g: 2 marbles
 

In simple words: Represent each marble with one circle symbol next to its respective weight.
Exam Tip: Always state the key clearly (e.g., Key: 1 circle = 1 marble) below or beside your pictograph.

Question 5. The following are the details of the number of students in a class of 30 students present during a week: Monday: 24, Tuesday: 20, Wednesday: 28, Thursday: 32, Friday: 24, Saturday: 28. Prepare a pictograph of these students. Use triangle symbol to represent four students.
Answer:
Calculate the number of triangle symbols (\(\Delta\)) needed for each day (Number of students \(\div 4\)):
- Monday: \(24 \div 4 = 6\) triangles
- Tuesday: \(20 \div 4 = 5\) triangles
- Wednesday: \(28 \div 4 = 7\) triangles
- Thursday: \(32 \div 4 = 8\) triangles
- Friday: \(24 \div 4 = 6\) triangles
- Saturday: \(28 \div 4 = 7\) triangles
 

In simple words: Since one triangle stands for 4 students, divide each day's attendance by 4 to find how many triangles to draw.
Exam Tip: Always write the symbol scale explicitly: "Scale: \(\Delta = 4\) students" at the top or bottom of your table.

Question 6. The total number of cricket grounds in four cricket playing nations of Asia are given below Country: India (60), Pakistan (15), Sri Lanka (10), Bangladesh (5). Prepare a pictograph of these cricket grounds. Use square symbol to represent 5 cricket grounds and answer the following questions: (i) How many symbols represent cricket grounds of Pakistan? (ii) Which country has the least number of cricket grounds? (iii) What is the difference between the number of cricket grounds in India and Pakistan.
Answer:
Calculate the number of square symbols (\(\square\)) needed for each country (Number of grounds \(\div 5\)):
- India: \(60 \div 5 = 12\) squares
- Pakistan: \(15 \div 5 = 3\) squares
- Sri Lanka: \(10 \div 5 = 2\) squares
- Bangladesh: \(5 \div 5 = 1\) square
 

(i) Number of symbols representing Pakistan = \(15 \div 5 = 3\) symbols.
(ii) Bangladesh has the least number of cricket grounds (5 grounds).
(iii) Difference between India and Pakistan = 60 - 15 = 45 grounds.
In simple words: Divide each country's total grounds by 5 to find the symbol count, then answer the questions directly from the given data.
Exam Tip: For difference questions, always subtract the smaller value from the larger value.

Question 7. The population of Delhi state in different census years is as given below? Census Year: 1961 (30), 1971 (55), 1981 (70), 1991 (110), 2001 (150). (Population in Lakhs) Represent the above information with the help of Bar Graph
Answer:
To represent this data on a bar graph:
1. Take Census Years along the horizontal axis (X-axis) with uniform spacing.
2. Take Population in Lakhs along the vertical axis (Y-axis) with an appropriate scale (e.g., 1 unit = 20 Lakhs or 1 cm = 20 Lakhs).
3. Draw rectangular bars of equal width for each year corresponding to their population heights: 30, 55, 70, 110, and 150.

In simple words: Draw vertical bars for each census year matching its population height on the scale.

Exam Tip: Label both axes clearly: write "Census Year" along the X-axis and "Population (in Lakhs)" along the Y-axis.

Question 8. The population of four major cities in India in a particular year is given below City: Mumbai (120), Kolkata (130), Delhi (150), Chennai (80). (Population in Lakhs) Construct a bar graph to represent the above data.
Answer:
To construct the bar graph:
1. Mark the cities (Mumbai, Kolkata, Delhi, Chennai) on the X-axis with equal gaps.
2. Mark Population in Lakhs on the Y-axis.
3. Draw bars corresponding to heights: Mumbai = 120, Kolkata = 130, Delhi = 150, Chennai = 80.

In simple words: Represent city populations with equal-width vertical bars against the Y-axis scale.

Exam Tip: Ensure all bars have identical width and are spaced uniformly across the X-axis.

Question 9. The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years: Year: 1992 (28), 1993 (33), 1994 (55), 1995 (55), 1996 (80). Represent the above data with the help of bar graph.
Answer:
To represent this bank loan data:
1. Place Years (1992 to 1996) along the X-axis.
2. Place Loan Amount (in crores of Rs.) along the Y-axis.
3. Draw bars for each year with heights corresponding to: 1992 = 28, 1993 = 33, 1994 = 55, 1995 = 55, 1996 = 80.

In simple words: Draw bars showing loan amounts for each year against the vertical scale.

Exam Tip: Notice that 1994 and 1995 have identical loan amounts (55 crores), so their bars will be of the exact same height.

Question 10. The following data shows the average age of men in various countries in a certain year: Country: India (55), Nepal (52), China (60), Pakistan (50), U.K (70), U.S.A (75). (Average Age in years) Represent the above information with the help of bar graph.
Answer:
To represent the average age data:
1. Plot the countries (India, Nepal, China, Pakistan, U.K, U.S.A) along the horizontal X-axis.
2. Plot Average Age (in years) along the vertical Y-axis.
3. Draw bars of equal width corresponding to each country's average age: 55, 52, 60, 50, 70, and 75.

In simple words: Construct bars representing the average age of men for each country against the vertical age scale.

Exam Tip: Clearly label axes with "Country" at the bottom and "Average Age (in years)" along the side.