Data Handling — Questions and Answers
Welcome to HSLC Guru. This page gives complete, worked solutions for ASSEB (Assam State School Education Board) Class 6 New Mathematics Chapter 4, Data Handling — every “Work it Out” exercise, the in-text examples, and a set of additional practice questions for English-medium students.
Summary
Any collection of information — such as facts, numbers, measures, observations or other descriptions of things — is called data. In this chapter we learn how to collect data, organise it into a table, and represent it in different ways. To count data quickly we use tally marks: one stroke ‘ | ‘ for each item, and the fifth stroke drawn diagonally across the previous four so that we can count in groups of five.
The number of times a particular value, event or piece of data occurs is called its frequency, and a table that shows these counts is a frequency distribution table. A pictograph represents data using pictures or symbols, where each symbol stands for a fixed quantity (called the scale). When the data is large we use a bar graph, which shows data through equally spaced bars of equal width; the length or height of each bar gives the frequency of that category.
Choosing a suitable scale, using distinct colours, and labelling the axes clearly are the artistic and aesthetic aspects that make a pictograph or bar graph appealing and easy to read. By reading pictographs and bar graphs accurately, we can quickly understand data and draw meaningful conclusions.
Summary: This page provides complete ASSEB Class 6 New Mathematics Chapter 4 “Data Handling” question answers for English-medium students. It covers collection and organisation of data, tally marks, frequency and frequency distribution tables, pictographs and bar graphs, with fully worked solutions to every Work it Out exercise, the in-text examples, and additional MCQ, fill-in-the-blank, true/false and short-answer questions.
Textbook Questions and Answers
Many questions in this chapter are based on the frequency distribution table below (Day of Birth of 30 students, from Table 2) —
| Day of Birth | Number of Students (Frequency) |
|---|---|
| Monday | 5 |
| Tuesday | 4 |
| Wednesday | 7 |
| Thursday | 3 |
| Friday | 4 |
| Saturday | 1 |
| Sunday | 6 |
In-text Questions on the Table
(a) On which day(s) were the same number of students born?
Answer: On Tuesday and Friday — the same number of students (4 each) were born.
(b) On which day were the maximum number of students born?
Answer: On Wednesday, when the maximum of 7 students were born.
In-text Questions on the Frequency Distribution Table
1. On which day of the week were the maximum number of students born?
Answer: Wednesday (7 students).
2. On which day of the week were the least number of students born?
Answer: Saturday (1 student).
3. How many students were born on Monday?
Answer: 5 students were born on Monday.
4. Find the days on which the same number of students were born.
Answer: Tuesday and Friday (4 each).
Example 1 (Pictograph of ages)
The ages (in years) of 40 students selected for the Talent Search Examination are shown as a pictograph. The frequency distribution is —
| Age (in years) | Number of Students |
|---|---|
| 9 | 11 |
| 10 | 12 |
| 11 | 9 |
| 12 | 5 |
| 13 | 3 |
(a) How many students are there of age less than 12 years?
Answer: Students aged 9, 10 and 11 = 11 + 12 + 9 = 32 students.
(b) How many students are there of age 9 years and 13 years together?
Answer: 11 + 3 = 14 students.
(c) How many students are there of maximum age?
Answer: The maximum age is 13 years, with 3 students.
(d) What is the difference between the number of students of maximum and minimum age?
Answer: Minimum age 9 years has 11 students and maximum age 13 years has 3 students. Difference = 11 − 3 = 8 students.
Example (Bar graph of games)
The number of students who participated in district-level competitions — Football 320, Hockey 240, Badminton 160, Cricket 480. Taking a scale of 40, the bar heights are Football 8 units, Hockey 6 units, Badminton 4 units and Cricket 12 units.
(a) Which game is played by the least number of students?
Answer: Badminton (160 students).
(b) Which game is played by the most number of students?
Answer: Cricket (480 students).
(c) What is the difference in the number of students between the game played by the most and the least number of students?
Answer: 480 − 160 = 320 students.
(d) Which game is played by less than 200 students?
Answer: Badminton (160 students).
Work it Out 4.1
1. The ages (in years) of 40 students of Classes VI, VII and VIII selected for the Talent Search Examination are arranged in ascending order: 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13. Fill in the blanks.
Answer:
- (a) The minimum age selected for the exam is 9 years.
- (b) The maximum age selected for the exam is 13 years.
- (c) There are 11 students of age 9 years.
- (d) The number of students of age more than 10 years (ages 11, 12, 13) = 9 + 5 + 3 = 17 students.
2. Can we arrange the above data in another way?
Answer: Yes. Placing a tally mark against each age and making a frequency distribution table makes the data more compact and easier to read, as shown below.
| Age (years) | Tally marks | Number of students |
|---|---|---|
| 9 | ||||/ ||||/ | | 11 |
| 10 | ||||/ ||||/ || | 12 |
| 11 | ||||/ |||| | 9 |
| 12 | ||||/ | 5 |
| 13 | ||| | 3 |
(Here ‘||||/’ denotes a bundle of five — four vertical strokes crossed by the fifth stroke.)
3. Using the same ages of 40 students, complete the tally-mark table and answer the questions.
Answer:
- (a) Tally marks — 10 years: ||||/ ||||/ || (12), 11 years: ||||/ |||| (9), 12 years: ||||/ (5), 13 years: ||| (3).
- (b) Total in each age group — 9 years: 11, 10 years: 12, 11 years: 9, 12 years: 5, 13 years: 3 (total 40 students).
- (i) Students of age less than 12 years = 11 + 12 + 9 = 32.
- (ii) Students of age 9 years and 13 years together = 11 + 3 = 14.
- (iii) Students in the highest age group (13 years) = 3.
- (iv) The age group with the least number of students is 13 years (3 students).
- (v) The age group with the most students is 10 years (12 students).
4. The number of family members of 30 students are: 5, 4, 6, 6, 8, 7, 4, 5, 10, 6, 6, 4, 7, 8, 6, 4, 10, 8, 7, 7, 6, 5, 5, 7, 10, 7, 8, 4, 8, 6. Arrange the number of members serially and show them using tally marks.
Answer:
| Number of members | Tally marks | Number of students |
|---|---|---|
| 4 | ||||/ | 5 |
| 5 | |||| | 4 |
| 6 | ||||/ || | 7 |
| 7 | ||||/ | | 6 |
| 8 | ||||/ | 5 |
| 10 | ||| | 3 |
Total = 5 + 4 + 7 + 6 + 5 + 3 = 30 students.
Work it Out 4.2
1. In a shop the number of bicycles sold in a week is shown by a pictograph (one bicycle symbol = 1 bicycle): Monday 6, Tuesday 5, Wednesday 5, Thursday 8, Friday 3, Saturday 2.
Answer:
- (a) The maximum number of bicycles was sold on Thursday (8).
- (b) Bicycles sold in the week = 6 + 5 + 5 + 8 + 3 + 2 = 29.
- (c) The same number of bicycles was sold on Tuesday and Wednesday (5 each).
- (d) On Saturday, 2 bicycles were sold.
- (e) Difference between maximum and minimum = 8 − 2 = 6.
2. The favourite subject of each student of a class (among Mathematics, Assamese, Science, Social Science and English) is shown by a pictograph (one symbol = 1 student): Mathematics 8, Assamese 12, Science 7, Social Science 8, English 6.
Answer:
- (a) Total number of students in the class = 8 + 12 + 7 + 8 + 6 = 41.
- (b) The subject liked by the most students is Assamese (12); the subject liked by the least students is English (6).
- (c) Students who like Science and English together = 7 + 6 = 13.
- (d) Students who like Mathematics = 8.
- (e) Assamese is liked by 6 more students than English (12 − 6 = 6).
3. The number of domestic animals kept by 5 families of a village: Budhin 10, Kanmai 8, Gomseng 5, Nazma 8, Nisha 11. Represent this data by a pictograph and answer the questions.
Answer: Taking any symbol (say one animal picture) = 1 animal, draw that many symbols against each family (Budhin 10, Kanmai 8, Gomseng 5, Nazma 8, Nisha 11) to get the pictograph.
- (a) The family with the most animals is Nisha (11).
- (b) Difference between highest and lowest = 11 − 5 = 6.
- (c) Nisha has 11 − 5 = 6 more animals than Gomseng.
- (d) Families with more than 5 animals: Budhin, Kanmai, Nazma and Nisha.
4. The quantity (in kg) of vegetables sold in the first four days of a week: Monday 6, Tuesday 8, Wednesday 5, Thursday 8. Using a suitable symbol, represent this data in a pictograph.
Answer: Taking one symbol (say a vegetable basket) = 1 kg, draw 6 symbols for Monday, 8 for Tuesday, 5 for Wednesday and 8 for Thursday to get the pictograph. (Tuesday and Thursday have the same quantity, 8 kg each.)
Work it Out 4.3
1. The year-wise number of babies vaccinated for polio over 5 years (data from a Panchayat) is given below. Taking 1 unit length = 100 babies, represent the data as a bar diagram and answer the questions.
| Year | 2014 | 2015 | 2016 | 2017 | 2018 |
|---|---|---|---|---|---|
| Number of babies | 570 | 680 | 720 | 780 | 800 |
Answer: Each bar height = number ÷ 100 units (e.g. 2014: 5.7 units, 2018: 8 units).
- (a) The highest number of babies were vaccinated in 2018 (800).
- (b) Babies vaccinated in 2015 and 2016 = 680 + 720 = 1400.
- (c) Difference between the maximum and minimum over 5 years = 800 − 570 = 230.
2. On World Environment Day the students of Classes Six to Ten planted saplings: Six 50, Seven 75, Eight 60, Nine 80, Ten 110. Draw a bar graph using a proper scale.
Answer: Taking 1 unit = 10 saplings, the bar heights are Six 5, Seven 7.5, Eight 6, Nine 8, Ten 11 units. Drawing equal-width bars of these heights gives the bar graph. Class Ten planted the most (110) and Class Six the least (50).
3. From Haren’s book-shop bar graph (first four months, scale 1 unit = 20 books), prepare the table and answer the questions.
Answer: Reading the bar graph gives the table —
| Month | Number of books sold |
|---|---|
| January | 80 |
| February | 120 |
| March | 60 |
| April | 80 |
- (a) The highest sales were in February (120 books).
- (b) Total books sold in April and March = 80 + 60 = 140.
- (c) Difference between January and March = 80 − 60 = 20.
4. The number of students of Classes Six to Ten present on Monday: Six 65, Seven 58, Eight 75, Nine 40, Ten 35. Prepare the bar graph and answer the questions.
Answer: Taking 1 unit = 5 students and drawing equal-width bars gives the bar graph.
- (a) The least number of students were present in Class Ten (35).
- (b) Total students present that day = 65 + 58 + 75 + 40 + 35 = 273.
- (c) Total present in Classes Nine and Ten = 40 + 35 = 75.
5. The number of girls of a school over 5 years: 2008 — 200, 2009 — 350, 2010 — 400, 2011 — 250, 2012 — 420. Draw a bar graph of the data.
Answer: Taking 1 unit = 50 girls, the bar heights are 2008: 4, 2009: 7, 2010: 8, 2011: 5, 2012: 8.4 units. Drawing equal-width bars of these heights gives the bar graph (highest in 2012 with 420 girls).
Climatic Data (reading bar graphs)
Month-wise average rainfall of Assam in a year (in mm, approx.): Jan 13, Feb 19, Mar 36, Apr 115, May 225, Jun 323, Jul 348, Aug 285, Sep 244, Oct 110, Nov 18, Dec 14.
(a) In which month is the average rainfall the highest?
Answer: July (348 mm).
(b) In which month is the average rainfall the lowest?
Answer: January (13 mm).
(c) In how many months is the average rainfall more than the average rainfall of the year?
Answer: The yearly average is about 146 mm. Rainfall exceeds this in May, June, July, August and September — 5 months.
(d) What is the average rainfall during the year?
Answer: The sum of the 12 monthly values = 1750 mm, so the average rainfall = $\frac{1750}{12} \approx 145.83$ mm (about 146 mm).
Month-wise average temperature of Assam in a year (in °C, approx.): Jan 19, Feb 22, Mar 27, Apr 28, May 30, Jun 30, Jul 29, Aug 29, Sep 29, Oct 26, Nov 23, Dec 20.
(a) In which month is the average temperature the lowest?
Answer: January (19 °C).
(b) What is the average temperature during the year?
Answer: The sum of the 12 monthly values = 312 °C, so the average temperature = $\frac{312}{12} = 26$ °C.
(c) In how many months is the average temperature more than the yearly average?
Answer: Temperature exceeds 26 °C in March, April, May, June, July, August and September — 7 months.
(d) In which month is the average temperature equal to the yearly average?
Answer: October (26 °C, equal to the yearly average).
Work it Out 4.4
1. To visually represent the heights of the mountains of the world, would you use a graph with vertical bars or horizontal bars? Why?
Answer: Vertical bars (columns). Height is measured upward from the ground, so vertical bars represent height naturally and clearly.
2. In your locality, collect data of the number of people whose age is 0–9, 10–19, 20–29, 30–39 and 40–49 (from 20 families only) and represent it using visually appealing bars.
Answer: This is a data-collection activity. Note the age of every member of 20 families, put a tally mark against each age group (0–9, 10–19, 20–29, 30–39, 40–49) and make a frequency distribution table. Then mark the age groups on the horizontal axis and the number of people on the vertical axis, choose a suitable scale, and draw equal-width bars of different colours to make an appealing bar graph. (The answer depends on the data you collect.)
Sample Pictograph and Bar Graph
Below, the Day of Birth data of 30 students (Monday 5, Tuesday 4, Wednesday 7, Thursday 3, Friday 4, Saturday 1, Sunday 6) is shown as a sample pictograph (each ● = 1 student) —
The same seven days, for 100 students (Monday 16, Tuesday 15, Wednesday 14, Thursday 19, Friday 16, Saturday 9, Sunday 11), shown as a sample bar graph (scale: 1 unit = 1 student) —
Additional Questions and Answers
Multiple Choice Questions (MCQ)
1. A collection of numbers, measures or observations is called —
(a) a table (b) data (c) a bar (d) a scale
Answer: (b) data.
2. In tally marks, how is the fifth stroke drawn?
(a) vertically (b) horizontally (c) diagonally across the previous four (d) as a circle
Answer: (c) diagonally across the previous four.
3. The number of times a particular value or piece of data occurs is called its —
(a) scale (b) unit (c) frequency (d) symbol
Answer: (c) frequency.
4. Representing data using pictures or symbols is called a —
(a) pictograph (b) bar graph (c) table (d) tally mark
Answer: (a) pictograph.
5. A graph that represents data using equally spaced bars of equal width is a —
(a) pictograph (b) bar graph (c) infographic (d) frequency
Answer: (b) bar graph.
6. In a bar graph, the length or height of a bar represents —
(a) the name of the category (b) the frequency of that category (c) the width of the bar (d) none of these
Answer: (b) the frequency of that category.
7. To represent data about heights, which graph is most suitable?
(a) vertical bars (b) horizontal bars (c) tally marks (d) a table
Answer: (a) vertical bars.
8. A bar graph with vertical bars is also called a —
(a) column graph (b) infographic (c) pictograph (d) tally chart
Answer: (a) column graph.
9. The artistic representation of large data using images, symbols and text is called —
(a) tally marks (b) unit (c) infographics (d) scale
Answer: (c) infographics.
10. In a pictograph, the quantity represented by each symbol is called the —
(a) scale (b) frequency (c) row (d) column
Answer: (a) scale.
Fill in the Blanks
- 1. Arranging data into rows and columns is called a ____. (table)
- 2. In tally marks, ‘||||/’ represents ____. (five (5))
- 3. In a bar graph, the width of all bars must be ____. (equal)
- 4. The value represented by each symbol in a pictograph is called the ____. (scale)
- 5. A table that shows frequencies is called a ____ table. (frequency distribution)
True or False
- 1. A single tally mark ‘ | ‘ represents one item. — True
- 2. In a bar graph, the gaps between the bars should be unequal. — False (the gaps must be equal).
- 3. A pictograph is always easy to draw for very large data. — False (it becomes difficult when the data is large or the frequency is not a multiple of the scale).
- 4. Frequency means how many times a value occurs. — True
- 5. The bars of a bar graph may be drawn vertically or horizontally. — True
Short Answer Questions
1. What is data?
Answer: Any collection of information — such as facts, numbers, measures, observations or descriptions of things — is called data.
2. What is the advantage of using tally marks?
Answer: Tally marks group data in fives, which makes counting quick and easy and helps us find the frequency of each value.
3. State one difference between a pictograph and a bar graph.
Answer: A pictograph shows data using the number of pictures or symbols, while a bar graph shows data using the length or height of equal-width bars. A bar graph is more convenient for large data.
4. Why is choosing an appropriate scale important when drawing a bar graph?
Answer: The scale decides the height of the bars. A suitable scale conveys the data accurately and attractively and makes the graph fit well within the available space.
Key Terms
| Term | Meaning |
|---|---|
| Data | A collection of numbers, measures or observations |
| Organisation of data | Arranging data into rows and columns (a table) |
| Tally marks | Strokes used for counting, bundled in fives |
| Frequency | The number of times a value or piece of data occurs |
| Frequency distribution table | A table that shows the frequency of each value |
| Pictograph | Data shown using pictures or symbols |
| Bar graph | Data shown using equally spaced bars of equal width |
| Scale | The quantity represented by one symbol or one unit of a bar |
| Unit | One step of the scale (one stroke / one symbol) |
| Column graph | A bar graph drawn with vertical bars |
| Infographics | An attractive visual representation of data using images, symbols and text |