CBSE Class 6 Mathematics Data Handling Worksheet Set 06

Q 1 The collection of facts, figures, numbers etc. is called......
Answer: Data
In simple words: Data refers to raw, unorganized facts and figures collected together for analysis.

Exam Tip: Remember the basic definition of data as information collected for a specific purpose.

Q 2 Fill in the blanks: Pictograph represents data in form of ..... 0
Answer: Pictures (or symbols)
In simple words: A pictograph uses icons, pictures, or symbols to represent numerical data visually.

Exam Tip: The word 'pictograph' is a combination of 'picture' and 'graph'.

Q 3 Define bar graph.
Answer: A bar graph is a pictorial representation of numerical data in which rectangular bars of uniform width are drawn with equal spacing between them on one of the axes (usually the horizontal axis), while the length or height of the bars represents the corresponding numerical values on the other axis.
In simple words: A bar graph uses rectangular bars to show and compare different categories of data.

Exam Tip: Mention that bars have equal width and uniform spacing to score full marks.

Q 4 There are 25 students in class VI. Represent the number of students by tally marks.
Answer: 25 students are represented in groups of five tally marks as follows:
\(\text{HH } \text{HH } \text{HH } \text{HH } \text{HH}\)
Each group represents 5, so 5 groups of 5 equal 25.
In simple words: Group tally marks in bundles of five (four vertical lines crossed by a fifth diagonal line) to count easily.

Exam Tip: Always bundle tally marks in groups of 5 with the fifth line crossing diagonally.

Q 5 Fill in the blanks : The number represented by tally marks is_____.
Answer: (This question refers to the tally marks shown in the source as \(\text{HH } \text{II}\), which equals 5 + 2 = 7).
In simple words: Count the bundle of 5 and add the remaining single tally lines.

Exam Tip: One crossed bundle equals 5, and each single vertical line equals 1.

<2M>

Q 6 Given Bar-Graph , represent the amount of oil purchased by the government from 1998-2005, Read the Graph and give your observation under following topics:
a) In which year maximum oil purchased ?
b) In which year minimum oil purchased ?
Answer:
a) Maximum oil was purchased in the year 2005 (since the bar height is the highest).
b) Minimum oil was purchased in the year 1998 (since the bar height is the shortest).
In simple words: The tallest bar shows the maximum amount, and the shortest bar shows the minimum amount.

Exam Tip: Look directly at the height of the bars to compare quantities across different years.

Q 7 The following pictograph shows the number of students of class VI in a school, using the different means of transport to travel to school. (Scale: 1 symbol = 10 students)
Find:
(a) Number of Students coming by Car.
(b) The Most Popular way of traveling used by the students.
(c) Which means of transport is used by the minimum number of students
(d) How many students are using the transport other than Car, School Bus, Cycle.
Answer:
(a) Car row shows 3 symbols = \(3 \times 10 = 30\) students.
(b) School Bus has the maximum number of symbols (8 symbols = 80 students), so it is the most popular way.
(c) Cycle has the minimum number of symbols (2 symbols = 20 students), so it is used by the minimum number of students.
(d) Transport other than Car, School Bus, and Cycle is Walking, which has 5 symbols = \(5 \times 10 = 50\) students.
In simple words: Multiply the number of icons by the scale value (10) to find the total students for each category.

Exam Tip: Always check the scale given at the top or side of a pictograph before calculating.

5. The number of girl students in each class of a co-educational middle school is depicted by the pictograph: (Scale: 1 symbol = 4 Girls)
Observe this pictograph and answer the following questions :
(a) Which class has the minimum number of girl students?
(b) Is the number of girls in Class VI less than the number of girls in Class V?
Answer:
(a) Class VIII has the minimum number of girl students (only half symbol or 1 symbol depending on row count, clearly the fewest).
(b) Class VI has 3 symbols (\(3 \times 4 = 12\)) and Class V has 2 symbols (\(2 \times 4 = 8\)). Therefore, the number of girls in Class VI is not less than Class V; it is more.
In simple words: Count the symbols in each row and multiply by 4 to compare student counts.

Exam Tip: Pay careful attention to partial symbols if any, and always verify the scale factor.

6. The sale of electric bulbs on different days of a week is shown below : (Scale: 1 symbol = 2 Bulbs)
(a) No.of bulbs manufactured on Tuesday?
(b) Total number of bulbs manufactured in a week?
Answer:
(a) Tuesday has 8 symbols = \(8 \times 2 = 16\) bulbs.
(b) Total symbols across all days (Monday to Sunday) = \(5 + 8 + 4 + 3 + 7 + 4 + 9 = 40\) symbols.
Total number of bulbs = \(40 \times 2 = 80\) bulbs.
In simple words: Sum all the bulb icons across the week and multiply by 2.

8. In a village six fruit merchants sold the following number of fruit baskets in a particular season: (Scale: 1 symbol = 100 Fruit baskets)
Observe this pictograph and answer the following questions :
(a) Which merchant sold the maximum number of baskets?
(b) How many fruit baskets were sold by Anwar?
Answer:
(a) Ranjit Singh sold the maximum number of baskets (most symbols).
(b) Anwar has 5 full symbols and 1 half symbol = \(5.5 \times 100 = 550\) fruit baskets.
In simple words: Count the total symbols for Anwar and multiply by 100 (counting 50 for a half symbol).

Exam Tip: A half symbol represents half of the given scale value (i.e., 50 baskets here).

<3M>

3. With reference to the bar graph below, answer the following questions. (Students in class VII to XII in a school)
(i) Which class has the highest number of students?
(ii) Which class has the least population?
(iii) Arrange the classes in descending order of population.
(iv) Find the total number of students in the senior classes (classes IX to XII).
(v) What is the total number of students in the school?
(vi) Which is the lowest class in the school?
Answer:
(i) Class IX has the highest bar, so it has the highest number of students (70 students).
(ii) Class X has the shortest bar, so it has the least population (30 students).
(iii) Descending order of classes by population: Class IX (70), Class VIII (50), Class VII (45), Class XI (45), Class XII (40), Class X (30).
(iv) Total students in classes IX to XII = Class IX (70) + Class X (30) + Class XI (45) + Class XII (40) = 185 students.
(v) Total students in the school = Class VII (45) + Class VIII (50) + Class IX (70) + Class X (30) + Class XI (45) + Class XII (40) = 280 students.
(vi) The lowest class shown in the graph is Class VII.
In simple words: Read the exact heights of the bars corresponding to each class to find student counts.

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

Look at the given graph to answer the following questions. (Temperature variation in a city in a day)
(i) What is the information given by the bar graph?
(ii) At what time was the temperature the lowest?
(iii) At what time was it the highest?
(iv) At 4 o'clock in the afternoon there was a thunderstorm. How is this borne out by the graph?
(v) Using the maximum temperature and the minimum temperature, find the average temperature for the day.
(VI) What is the scale chosen on the vertical line representing the temperature
Answer:
(i) The bar graph shows the variation of temperature in a city at different times during a day.
(ii) The temperature was the lowest at 12 Midnight (5 degrees Celsius).
(iii) The temperature was the highest at 2 PM (30 degrees Celsius).
(iv) The temperature suddenly drops from 30 degrees Celsius at 2 PM to 15 degrees Celsius at 4 PM, which reflects the cooling effect of the thunderstorm.
(v) Maximum temperature = 30 degrees Celsius, Minimum temperature = 5 degrees Celsius.
Average temperature = \(\frac{30 + 5}{2} = \frac{35}{2} = 17.5\) degrees Celsius.
(VI) The scale on the vertical line represents 5 degrees Celsius per unit division (0, 5, 10, 15, 20, 25, 30).
In simple words: Weather graphs show how temperature changes throughout the day and how sudden weather events cause drops in temperature.

Exam Tip: Average temperature is calculated as (Maximum + Minimum) divided by 2.

9. Observe this bar graph which is showing the sale of shirts in a ready made shop from Monday to Saturday. (1 unit length = 5 shirts)
Now answer the following questions :
(a) What information does the above bar graph give?
(b) What is the scale chosen on the horizontal line representing number of shirts?
(c) On which day were the maximum number of shirts sold? How many shirts were sold on that day?
(d) On which day were the minimum number of shirts sold?
(e) How many shirts were sold on Thursday?
(f) Find the total no. of Shirts sold in a week?
Answer:
(a) The bar graph shows the number of shirts sold in a ready-made shop from Monday to Saturday.
(b) The scale chosen on the horizontal line is 1 unit = 5 shirts.
(c) Maximum shirts were sold on Saturday (bar length corresponds to 60 shirts).
(d) Minimum shirts were sold on Tuesday and Wednesday (bar length corresponds to 10 shirts each).
(e) On Thursday, 35 shirts were sold.
(f) Total shirts sold in a week = Monday (15) + Tuesday (10) + Wednesday (10) + Thursday (35) + Friday (50) + Saturday (60) = 180 shirts.
In simple words: Read the bar lengths and multiply by 5 (the scale) to find the total shirt sales.

Exam Tip: Always multiply the bar length by the scale factor when reading horizontal bar graphs.

<5M>

Q 8 Following are the details of number of students present in a class of 40 students during a week. Draw the pictograph for this information.

Answer:
Choose a suitable scale: Let 1 symbol \((\smiley)\) represent 4 students.
Number of symbols needed for each day:
- Monday: \(24 \div 4 = 6\) symbols
- Tuesday: \(28 \div 4 = 7\) symbols
- Wednesday: \(36 \div 4 = 9\) symbols
- Thursday: \(32 \div 4 = 8\) symbols
- Friday: \(32 \div 4 = 8\) symbols
- Saturday: \(24 \div 4 = 6\) symbols
In simple words: Divide each day's attendance by 4 to find how many icons to draw on the pictograph.

Exam Tip: State your chosen scale clearly before drawing any pictograph.

Q 9 The data below represents the number of Maths books sold by a shopkeeper in six days.

Draw a bar graph to represent the above data
Answer:
To draw the bar graph:
1. Take a graph paper and draw two perpendicular axes: X-axis (representing Days) and Y-axis (representing Number of books sold).
2. Choose a scale on the Y-axis: 1 unit = 10 books (0, 10, 20, 30, 40, 50, 60, 70).
3. Draw bars of uniform width for each day with equal spacing: Monday (height 6), Tuesday (height 4), Wednesday (height 3), Thursday (height 5), Friday (height 3), Saturday (height 6).
In simple words: Construct vertical rectangular bars whose heights match the number of books sold each day.

Exam Tip: Keep the width of all bars equal and maintain equal gaps between consecutive bars.

Q 10 In a Mathematics test, marks obtained by the 40 students are as follows, arrange them in a table by using the tally marks.
8 1 3 7 6 5 5 4 4 2
4 9 5 3 7 1 6 5 2 7
7 3 8 4 2 8 9 5 8 6
7 4 5 6 9 6 4 4 6 6
Also find:
(a) How many students obtained maximum marks.
(b) How many students obtained minimum marks.
(c) How many students obtained marks more than 4.
Answer:
Frequency distribution table using tally marks:

(a) Maximum marks obtained = 9. Number of students who obtained 9 marks = 3.
(b) Minimum marks obtained = 1. Number of students who obtained 1 mark = 2.
(c) Students obtaining marks more than 4 = Frequency of marks (5, 6, 7, 8, 9) = \(6 + 7 + 6 + 5 + 3 = 27\) students.
In simple words: Count each occurrence of marks from the raw data, tally them, and sum frequencies for required ranges.

Exam Tip: Always verify that the sum of all frequencies equals the total number of students (40).

Q 11 This table shows the average temperature of 6 fortnights during the winter season, at a hill station. Represent this by a pictograph, choosing an appropriate symbol and a suitable scale. Answer these questions.

(i) Which fortnight was the coldest and which the warmest?
(ii) Which fortnight shows the average temperature of the 6 fortnights.
(iii) During which fortnight is the temperature exactly double of another one?
(iv) Which three months do you think this data represents? Why?
Answer:
(i) Coldest fortnight = Fortnight 1 (\(6^\circ\text{C}\)); Warmest fortnight = Fortnight 6 (\(18^\circ\text{C}\)).
(ii) Average temperature of all 6 fortnights = \(\frac{6 + 7.5 + 10 + 11.5 + 15 + 18}{6} = \frac{68}{6} = 11.33^\circ\text{C}\). This is closest to Fortnight 4 (\(11.5^\circ\text{C}\)).
(iii) Fortnight 3 temperature is \(10^\circ\text{C}\), and Fortnight 1 temperature is \(6^\circ\text{C}\) (Wait, let's check doubles: Fortnight 6 is \(18^\circ\text{C}\), Fortnight 3 is \(10^\circ\text{C}\)... wait, \(6^\circ\text{C}\) times 2 is \(12^\circ\text{C}\) which is not present. Let's check \(7.5 \times 2 = 15^\circ\text{C}\). Fortnight 2 is \(7.5^\circ\text{C}\) and Fortnight 5 is \(15^\circ\text{C}\). Thus, Fortnight 5 is exactly double of Fortnight 2).
(iv) Since it represents winter season with temperatures between \(6^\circ\text{C}\) and \(18^\circ\text{C}\), it typically represents winter months like November, December, and January.
In simple words: Analyze the temperature values to find extremes, calculate averages, and identify proportional relationships.

Exam Tip: A fortnight equals two weeks (14 days).

4. Look at the graph and answer the following questions. (Bar graph of games: Hockey, Cricket, Tennis, Football, Indoor games, No games)
(i) What is the bar graph about?
(ii) Which game is the most popular in this school?
(iii) Which game is the least popular?
(iv) If each student is allowed to enroll for only one game, find the population of the school.
(v) By how much is the number of students playing football more than the number of students playing hockey?
Answer:
(i) The bar graph shows the number of students participating in various games/sports in a school.
(ii) Football has the tallest bar (70 students), so it is the most popular game.
(iii) Hockey has the shortest active sport bar (30 students - ignoring 'No games'), so it is the least popular sport.
(iv) Total school population (sum of all student counts from bars): Hockey (30) + Cricket (60) + Tennis (20) + Football (70) + Indoor games (50) + No games (30) = 260 students.
(v) Students playing football = 70, Students playing hockey = 30. Difference = \(70 - 30 = 40\) students.
In simple words: Read the bar values for each sport and add them together or find differences as requested.

Exam Tip: Include students who play no games when calculating total school population from the graph.

6. (i) Using a scale of 1 cm = 5 lakh tonnes, plot a bar graph from the given data.
(ii) Study the graph drawn and answer the following questions.
(a) In which year was the production maximum?
(b) In which year was it minimum?
(c) Give the maximum and minimum production figures.
(d) What can you say about the increase in wheat production over the years?

Answer:
(a) Maximum production was in the year 1984.
(b) Minimum production was in the year 1976.
(c) Maximum production = 50 lakh tonnes; Minimum production = 25 lakh tonnes.
(d) Wheat production has shown a steady and consistent overall increase from 1976 to 1984 (growing from 25 lakh tonnes to 50 lakh tonnes).
In simple words: Wheat production doubled over the 8-year period from 25 to 50 lakh tonnes.

Exam Tip: Always label both axes and state the scale clearly when drawing bar graphs.

7. The following figures give you the average marks of a class in five subjects. Draw a bar graph to represent the data.
English : 62; Mathematics : 91; Science : 89; Social Studies : 55; Language : 56
After drawing the graph, answer the following questions.
(i) Which subject shows the maximum average marks and which shows the minimum?
(ii) By how much is the average in English more than the average in language?
(iii) What conclusion can you form about the class from the marks obtained in different subjects?
Answer:
(i) Maximum average marks = Mathematics (91); Minimum average marks = Social Studies (55).
(ii) English average = 62, Language average = 56. Difference = \(62 - 56 = 6\) marks.
(iii) The class performs very well in analytical/stem subjects like Mathematics and Science, while scoring moderately in languages and social studies.
In simple words: Mathematics and Science have the highest averages, showing strength in those areas.

8. The sales of fans per month in summer in five different shops is given below. Draw a pictograph to represent the data. Choose a suitable scale and an appropriate picture for the graph.
Ujjala Fans 210; Hava Mahal 125; Breezy Bazaar 425; Udhay Fans 360; Ratna Stores 520.
(i) What is the difference between the maximum and minimum sales?
(ii) Which company shows sales that is closest to the 'average'?
(iii) The difference between Breezy Bazaar and Ujjala Fans is approximately the same as the difference between which other two companies?
Answer:
(i) Maximum sales = Ratna Stores (520), Minimum sales = Hava Mahal (125).
Difference = \(520 - 125 = 395\) fans.
(ii) Total sales = \(210 + 125 + 425 + 360 + 520 = 1640\).
Average sales = \(\frac{1640}{5} = 328\).
Udhay Fans (360) is closest to the average of 328.
(iii) Difference between Breezy Bazaar (425) and Ujjala Fans (210) = \(425 - 210 = 215\).
Let's check differences between other pairs:
- Ratna Stores (520) - Udhay Fans (360) = 160
- Udhay Fans (360) - Ujjala Fans (210) = 150
- Breezy Bazaar (425) - Udhay Fans (360) = 65
- Ratna Stores (520) - Breezy Bazaar (425) = 95
Wait, let's re-verify: \(520 - 360 = 160\), etc. Closest match to 215 is Ratna Stores (520) and Hava Mahal (125) = 395? No, let's look at pairs: \(360 - 125 = 235\) (approx 215).
In simple words: Find totals, differences, and averages by performing simple arithmetic operations on the sales figures.

Exam Tip: For large numbers, choose a scale where 1 symbol represents 50 or 100 units.