Sum of observations divided by Number of observations.

Exercise Solutions Available

Step-by-step answers for all textbook questions in this chapter

Statistics — Exercise Solutions

Q: What is the mode?

The value that occurs most frequently in a data set.

How to Use This Page

This page covers every exercise from the TN Class 6 Maths Chapter 5 (Statistics) textbook. Each section starts with a quick recap of the key concept, followed by detailed step-by-step solutions. Work through the solutions only after attempting the problems yourself — that is how you build real understanding.

Key Concepts (Quick Recap)

Data and Tally Marks

Data: A collection of numbers or facts gathered to give meaningful information.
Raw data: Data collected in its original, unorganised form.
Array: Arranging data in ascending or descending order.
Tally marks: A quick way to record and count frequencies. Every fifth tally mark crosses the previous four diagonally (|||| = 4, plus one diagonal makes 5).

Pictographs

A pictograph uses pictures or symbols to represent data.
Each picture stands for a fixed number of objects — this is called scaling.
Always check the key (scale) before reading a pictograph.

Bar Graphs

A bar graph displays data using rectangular bars of uniform width.
The length (or height) of each bar is proportional to the value it represents.
Bars can be drawn horizontally or vertically.
The gap between consecutive bars must be equal.

Mean

The mean (or average) of a set of observations is:

Mean = (Sum of all observations) / (Number of observations)

FormulaMean = Σxᵢ / n

Median

The median is the middle value when data is arranged in ascending or descending order.

If n is odd: Median = value at position (n + 1)/2
If n is even: Median = average of values at positions n/2 and (n/2 + 1)

Mode

The mode is the value that occurs most frequently in a data set.

A data set can have no mode (all values occur equally), one mode (unimodal), or more than one mode (bimodal, trimodal, etc.).

Exercise 5.1 — Data and Tally Marks

Q1. What is data?

SolutionData is a collection of numbers or facts gathered to give meaningful information. For example, marks scored by students in a class, heights of players in a team, or temperatures recorded over a week.

AnswerData is a collection of numbers gathered to give meaningful information.

Q2. Arrange the following data in ascending order: 15, 8, 22, 3, 11, 7

SolutionTo arrange in ascending order, we list the numbers from smallest to largest.

The smallest number is 3, then 7, then 8, then 11, then 15, and the largest is 22.

Answer3, 7, 8, 11, 15, 22

Q3. The following data shows the number of siblings of 10 students: 2, 1, 3, 2, 0, 1, 2, 3, 1, 2. Organise this data using tally marks.

SolutionWe first identify the distinct values and then count how many times each appears.

Number of siblings	Tally marks	Frequency
0	\		1
1	\	\	\		3
2	\	\	\		4
3	\	\		2

Verification: 1 + 3 + 4 + 2 = 10 (matches total number of students).

AnswerThe tally table is shown above. The most common number of siblings is 2 (frequency 4).

Q4. The favourite fruits of 20 students are: Apple, Banana, Apple, Mango, Banana, Apple, Mango, Banana, Apple, Orange, Mango, Banana, Apple, Orange, Mango, Banana, Apple, Mango, Banana, Mango. Represent using tally marks.

Solution

Fruit	Tally marks	Frequency
Apple	\	\	\	\	6
Banana	\	\	\	\	6
Mango	\	\	\	\	6
Orange	\	\		2

Verification: 6 + 6 + 6 + 2 = 20.

AnswerApple = 6, Banana = 6, Mango = 6, Orange = 2.

Q5. What are tally marks? Explain with an example.

Solution: Tally marks are a simple method of recording and counting data. We use vertical lines (\	) to represent counts. After every four vertical lines, the fifth count is represented by a diagonal line crossing the four. This makes counting easier because groups of five can be quickly identified.

Example: To represent 8 using tally marks, we write `				+			` — that is, one group of five (four verticals crossed by one diagonal) and three more verticals.

AnswerTally marks are a counting method using vertical lines, with every fifth mark crossing the previous four diagonally.

Q6 (MCQ). Tally marks for the number 7 in standard form is:

(a)							(b)						(c)							(d)

Solution: In standard tally notation, 7 is represented as one group of five (				with a diagonal crossing) plus two more verticals. This is written as `						`.

Answer: (b)

Q7 (MCQ). Tally marks								represent the number:

(a) 8 (b) 4 (c) 9 (d) 5

Solution: The first group `				`with a diagonal is 5, and the second group`				`with a diagonal is another 4 (or possibly 5 depending on notation). In standard representation,`								` means 5 + 4 = 9.

Answer(c) 9

Q8 (MCQ). The plural of the word 'datum' is:

(a) datums (b) datam (c) data (d) dates

SolutionThe singular form of data is "datum." The plural form is "data."

Answer(c) data

Exercise 5.2 — Pictographs

Q1. The following pictograph shows the number of books read by four students. Each book symbol represents 2 books.

Student	Books
Arun	📕📕📕
Bharat	📕📕📕📕📕
Chitra	📕📕
Deepa	📕📕📕📕

How many books did each student read?

SolutionEach book symbol = 2 books.

Arun: 3 × 2 = 6 books
Bharat: 5 × 2 = 10 books
Chitra: 2 × 2 = 4 books
Deepa: 4 × 2 = 8 books

AnswerArun read 6, Bharat read 10, Chitra read 4, Deepa read 8 books.

Q2. A pictograph shows that a farmer grew different crops. If one symbol represents 5 tonnes, and the farmer has 4 symbols for rice, 2 symbols for wheat, and 3 symbols for maize, find the quantity of each crop.

SolutionEach symbol = 5 tonnes.

Rice: 4 × 5 = 20 tonnes
Wheat: 2 × 5 = 10 tonnes
Maize: 3 × 5 = 15 tonnes

AnswerRice = 20 tonnes, Wheat = 10 tonnes, Maize = 15 tonnes.

Q3. In a pictograph, one symbol represents 10 students. If Class A has 3.5 symbols, how many students are in Class A?

SolutionOne symbol = 10 students.

Number of students = 3.5 × 10 = 35

Answer35 students

Q4. Draw a pictograph for the following data using an appropriate symbol. Number of vehicles passing a signal in a week: Monday = 20, Tuesday = 30, Wednesday = 25, Thursday = 15, Friday = 35. Take one vehicle symbol = 5 vehicles.

Solution

Monday: 20 / 5 = 4 symbols
Tuesday: 30 / 5 = 6 symbols
Wednesday: 25 / 5 = 5 symbols
Thursday: 15 / 5 = 3 symbols
Friday: 35 / 5 = 7 symbols

The pictograph can be drawn using a car symbol where each symbol = 5 vehicles.

AnswerMonday: 4 symbols, Tuesday: 6 symbols, Wednesday: 5 symbols, Thursday: 3 symbols, Friday: 7 symbols.

Q5 (MCQ). The representation of one picture to many objects in a pictograph is called:

(a) Picture (b) Symbol (c) Scaling (d) Frequency

SolutionWhen one picture represents a fixed number of objects, this is called scaling. For example, if one tree symbol represents 100 trees, the scale is 1 symbol = 100 objects.

Answer(c) Scaling

Q6 (MCQ). In a pictograph, if one symbol = 10 items, then what is the representation of one picture to many objects called?

(a) Picture (b) Frequency (c) Scaling (d) Tally mark

SolutionThe method of using one picture to represent multiple objects is called scaling.

Answer(c) Scaling

Q7 (MCQ). A pictograph is also known as:

(a) Bar graph (b) Pictogram (c) Pie chart (d) Histogram

SolutionA pictograph uses pictures/symbols to represent data. It is also called a pictogram.

Answer(b) Pictogram

Exercise 5.3 — Bar Graphs

Q1. The following table shows the number of students absent in a class during a week. Draw a bar graph.

Day	Monday	Tuesday	Wednesday	Thursday	Friday
Students absent	5	3	7	2	6

Solution

1. Draw the x-axis (horizontal) and label it with the days of the week. 2. Draw the y-axis (vertical) and choose a suitable scale. Here, 1 unit = 1 student absent. 3. Draw bars of equal width for each day:

4. Keep equal spacing between bars. 5. Give the bar graph a title: "Number of Students Absent in a Week."

Monday: height = 5 units
Tuesday: height = 3 units
Wednesday: height = 7 units
Thursday: height = 2 units
Friday: height = 6 units

AnswerThe bar graph shows Wednesday had the most absences (7) and Thursday had the least (2).

Q2. Read the bar graph and answer: The bar graph shows the favourite sports of 40 students. Cricket = 15, Football = 10, Hockey = 5, Basketball = 7, Volleyball = 3. Which sport is most popular? Which is least popular?

Solution

Most popular: The sport with the highest bar. Cricket has the tallest bar at 15 students.
Least popular: The sport with the shortest bar. Volleyball has the shortest bar at 3 students.

AnswerMost popular = Cricket (15 students); Least popular = Volleyball (3 students).

Q3. The bar graph shows marks obtained by a student in five subjects: Tamil = 70, English = 65, Maths = 90, Science = 80, Social Science = 75. What are the total marks and average marks?

Solution

Total marks = 70 + 65 + 90 + 80 + 75 = 380

Average marks = Total / Number of subjects = 380 / 5 = 76

AnswerTotal marks = 380, Average marks = 76.

Q4. The number of books sold in a bookshop from Monday to Saturday is: Monday = 20, Tuesday = 35, Wednesday = 30, Thursday = 25, Friday = 45, Saturday = 50. Draw a bar graph.

Solution

1. Draw x-axis (days) and y-axis (number of books). 2. Choose scale: 1 unit = 5 books (or 1 unit = 10 books for a compact graph). 3. Draw bars for each day:

4. Maintain equal width and equal spacing between bars. 5. Title: "Books Sold in a Week."

Monday: 20 books → height = 4 units (if 1 unit = 5 books)
Tuesday: 35 books → height = 7 units
Wednesday: 30 books → height = 6 units
Thursday: 25 books → height = 5 units
Friday: 45 books → height = 9 units
Saturday: 50 books → height = 10 units

AnswerBar graph drawn with Saturday showing the highest sales (50) and Monday the lowest (20).

Q5 (MCQ). A bar graph can be drawn using:

(a) Only horizontal bars (b) Only vertical bars (c) Only diagonal bars (d) Either horizontal or vertical bars

SolutionA bar graph can be drawn with bars going either horizontally or vertically. Both orientations are valid representations of data.

Answer(d) Either horizontal or vertical bars

Q6 (MCQ). In a bar graph, the spaces between the bars:

(a) vary (b) are the same (c) are zero (d) depend on data

SolutionIn a bar graph, the spacing between consecutive bars must be uniform (the same). This is a standard rule for drawing bar graphs.

Answer(b) are the same

Exercise 5.4 — Mean, Median, Mode

Q1. Find the mean of the following data: 6, 8, 10, 12, 14

Solution

Mean = (Sum of observations) / (Number of observations)

Sum = 6 + 8 + 10 + 12 + 14 = 50

Number of observations = 5

Mean = 50 / 5 = 10

AnswerMean = 10

Q2. Find the mean of the first five natural numbers.

Solution

The first five natural numbers are: 1, 2, 3, 4, 5

Sum = 1 + 2 + 3 + 4 + 5 = 15

Number of observations = 5

Mean = 15 / 5 = 3

AnswerMean = 3

Q3. The mean of 6 numbers is 15. Find the sum of these 6 numbers.

Solution

Mean = Sum / Number of observations

15 = Sum / 6

Sum = 15 × 6 = 90

AnswerThe sum of the 6 numbers is 90.

Q4. Find the median of: 12, 7, 15, 9, 21

Solution

Step 1: Arrange in ascending order: 7, 9, 12, 15, 21

Step 2: Number of observations n = 5 (odd)

Step 3: Median = value at position (n + 1)/2 = (5 + 1)/2 = 3rd position

The 3rd value is 12.

AnswerMedian = 12

Q5. Find the median of: 3, 5, 7, 9, 11, 13

Solution

Step 1: Data is already in ascending order: 3, 5, 7, 9, 11, 13

Step 2: Number of observations n = 6 (even)

Step 3: Median = average of values at positions n/2 and (n/2 + 1)

Positions: 6/2 = 3rd and (6/2 + 1) = 4th

3rd value = 7, 4th value = 9

Median = (7 + 9) / 2 = 16 / 2 = 8

AnswerMedian = 8

Q6. Find the mode of: 3, 5, 7, 5, 9, 5, 11

Solution

Count the frequency of each value:

3 appears 1 time
5 appears 3 times
7 appears 1 time
9 appears 1 time
11 appears 1 time

The value with the highest frequency is 5 (appears 3 times).

AnswerMode = 5

Q7. Find the mode of: 2, 4, 6, 8, 10

Solution

Count the frequency of each value:

Each value (2, 4, 6, 8, 10) appears exactly once. No value occurs more frequently than the others.

AnswerNo mode (all values occur equally).

Q8. The marks of 7 students are: 25, 30, 35, 30, 40, 30, 45. Find the mean, median, and mode.

Solution

Mean: Sum = 25 + 30 + 35 + 30 + 40 + 30 + 45 = 235 Mean = 235 / 7 = 33.57 (approx 33.6)

Median: Arrange in ascending order: 25, 30, 30, 30, 35, 40, 45 n = 7 (odd), Median = value at (7 + 1)/2 = 4th position = 30

Mode: 30 appears 3 times (most frequent).

AnswerMean ≈ 33.6, Median = 30, Mode = 30

Q9. True or False: Ruby and Kuzhali save the same amount. The savings data is: Ruby saves Rs. 50, Rs. 60, Rs. 40, Rs. 50, Rs. 50; Kuzhali saves Rs. 55, Rs. 50, Rs. 50, Rs. 55, Rs. 40.

Solution

Ruby's total savings = 50 + 60 + 40 + 50 + 50 = 250 Ruby's mean savings = 250 / 5 = 50

Kuzhali's total savings = 55 + 50 + 50 + 55 + 40 = 250 Kuzhali's mean savings = 250 / 5 = 50

Both have the same mean savings of Rs. 50.

AnswerTrue — Ruby and Kuzhali save the same average amount (Rs. 50 each).

Q10. The weights (in kg) of 8 students are: 35, 40, 38, 42, 35, 39, 40, 35. Find the mean, median, and mode.

Solution

Mean: Sum = 35 + 40 + 38 + 42 + 35 + 39 + 40 + 35 = 304 Mean = 304 / 8 = 38

Median: Arrange in ascending order: 35, 35, 35, 38, 39, 40, 40, 42 n = 8 (even), Median = average of 4th and 5th values = (38 + 39) / 2 = 77 / 2 = 38.5

Mode: 35 appears 3 times (most frequent).

AnswerMean = 38, Median = 38.5, Mode = 35

MCQs from All Exercises

Q1. The mean of 4, 6, 8 is:

(a) 4 (b) 6 (c) 8 (d) 18

SolutionMean = (4 + 6 + 8) / 3 = 18 / 3 = 6

Answer(b) 6

Q2. The median of 2, 5, 3, 7, 1 is:

(a) 3 (b) 5 (c) 1 (d) 7

SolutionArrange in ascending order: 1, 2, 3, 5, 7. n = 5 (odd). Median = value at (5+1)/2 = 3rd position = 3.

Answer(a) 3

Q3. The mode of 2, 3, 2, 5, 2, 7 is:

(a) 3 (b) 5 (c) 7 (d) 2

Solution2 appears 3 times, which is more frequent than any other value.

Answer(d) 2

Q4. Data in its original form is called:

(a) Array (b) Raw data (c) Frequency (d) Tally marks

SolutionData collected in its original, unorganised form is called raw data.

Answer(b) Raw data

Q5. Arranging data in ascending or descending order is called:

(a) Grouping (b) Scaling (c) Array (d) Tally

SolutionWhen data is arranged in order (ascending or descending), it is called an array.

Answer(c) Array

Additional Questions

Q1. Define data.

SolutionData is a collection of numbers gathered to give meaningful information. Data can come from surveys, experiments, observations, or records.

AnswerData is a collection of numbers gathered to give meaningful information.

Q2. How can data be arranged in tabular form?

SolutionData can be arranged in a tabular form using tally marks. Each item's frequency is counted and recorded using vertical lines (tally marks). Every fifth tally crosses the previous four diagonally for easy counting.

AnswerData can be arranged in tabular form using tally marks to record frequencies.

Q3. Represent 8 occurrences using tally marks.

Solution: In tally mark notation, we group in fives. The first five are represented as `				` (four vertical lines crossed by a diagonal). Then the remaining three are shown as three vertical lines.

So 8 = `				+			` (one group of 5 plus 3 more).

Answer: 8 in tally marks = `							` (one complete group of 5 plus 3 individual marks)

Q4. The following data shows the number of children in 12 families: 2, 3, 1, 4, 2, 3, 2, 1, 3, 2, 4, 2. Arrange this data in a frequency table using tally marks.

Solution

Number of children	Tally marks	Frequency
1	\	\		2
2	\	\	\	\		5
3	\	\	\		3
4	\	\		2

Verification: 2 + 5 + 3 + 2 = 12 families.

AnswerThe most common number of children per family is 2 (frequency 5).

Q5. A pictograph shows ice cream sales. One ice cream symbol = 10 ice creams. Shop A has 3 symbols, Shop B has 5 symbols, Shop C has 4.5 symbols, and Shop D has 2 symbols. Find the total ice creams sold.

Solution

Shop A: 3 × 10 = 30
Shop B: 5 × 10 = 50
Shop C: 4.5 × 10 = 45
Shop D: 2 × 10 = 20

Total = 30 + 50 + 45 + 20 = 145

AnswerTotal ice creams sold = 145

Q6. The heights of 5 plants (in cm) are: 12, 15, 10, 18, 20. Find the mean height.

Solution

Sum = 12 + 15 + 10 + 18 + 20 = 75

Mean = 75 / 5 = 15

AnswerMean height = 15 cm

Q7. The ages of 6 children are: 8, 10, 8, 12, 8, 14. Find the mean, median, and mode.

Solution

Mean: Sum = 8 + 10 + 8 + 12 + 8 + 14 = 60 Mean = 60 / 6 = 10

Median: Arrange in ascending order: 8, 8, 8, 10, 12, 14 n = 6 (even), Median = average of 3rd and 4th values = (8 + 10) / 2 = 9

Mode: 8 appears 3 times (most frequent).

AnswerMean = 10, Median = 9, Mode = 8

Q8. A bar graph shows the number of cars sold by a dealer from Monday to Saturday: Monday = 8, Tuesday = 12, Wednesday = 6, Thursday = 10, Friday = 15, Saturday = 18. On which day were the most cars sold? What is the total number of cars sold?

Solution

The tallest bar represents the most cars sold: Saturday = 18 cars.

Total cars sold = 8 + 12 + 6 + 10 + 15 + 18 = 69

AnswerMost cars sold on Saturday (18). Total cars sold = 69.

Q9. The mean of 5 numbers is 20. If one more number 26 is added, what is the new mean?

Solution

Sum of 5 numbers = 5 × 20 = 100

New sum = 100 + 26 = 126

New number of observations = 6

New mean = 126 / 6 = 21

AnswerNew mean = 21

Q10. Find the median and mode of: 14, 14, 15, 16, 14, 17, 15

Solution

Median: Arrange in ascending order: 14, 14, 14, 15, 15, 16, 17 n = 7 (odd), Median = value at (7+1)/2 = 4th position = 15

Mode:

14 appears 3 times
15 appears 2 times
16 appears 1 time
17 appears 1 time

14 appears most frequently.

AnswerMedian = 15, Mode = 14

Q11. Draw a bar graph for the following data of Mathematics books sold on six days:

Day	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
Books sold	25	40	30	20	45	50

Solution

1. Draw x-axis and label the six days. 2. Draw y-axis and choose scale: 1 unit = 5 books (so maximum value 50 fits well). 3. Draw bars of equal width:

4. Keep equal spacing between bars. 5. Title: "Mathematics Books Sold During a Week."

Monday: 25 books → height = 5 units
Tuesday: 40 books → height = 8 units
Wednesday: 30 books → height = 6 units
Thursday: 20 books → height = 4 units
Friday: 45 books → height = 9 units
Saturday: 50 books → height = 10 units

AnswerThe bar graph shows Saturday had the highest sales (50) and Thursday had the lowest (20).

Q12. The bar graph shows the number of visitors to Mahabalipuram over five months:

Month	January	March	April	May	June
Visitors	2000	2000	3500	2500	1500

Answer the following:

(a) How many visitors came in April?

SolutionRead the bar for April from the graph. The height corresponds to 3500.

Answer3500 visitors

(b) How many more visitors came in May than January?

SolutionVisitors in May = 2500. Visitors in January = 2000.

Difference = 2500 − 2000 = 500

Answer500 more visitors in May than January.

(c) Which two months had the same number of visitors?

SolutionLooking at the data, January and March both have 2000 visitors. Their bars are of equal height.

AnswerJanuary and March (both 2000 visitors)

(d) How many more visitors came in April than January?

SolutionApril = 3500, January = 2000.

Difference = 3500 − 2000 = 1500

Answer1500 more visitors in April than January.

(e) What is the total number of visitors across all five months?

SolutionTotal = 2000 + 2000 + 3500 + 2500 + 1500 = 11,500

AnswerTotal visitors = 11,500

Common Mistakes

1. Forgetting to arrange data before finding the median. Always sort data in ascending or descending order first. The median of {12, 7, 15, 9, 21} is not 15 (the middle of the unsorted list). It is 12 (the middle of the sorted list: 7, 9, 12, 15, 21).

2. Confusing mean, median, and mode. Mean is the average (sum divided by count). Median is the middle value after sorting. Mode is the most frequently occurring value. They are often different numbers for the same data set.

3. Drawing bars of unequal width in a bar graph. All bars in a bar graph must have the same width. Only the height (or length) varies to represent different values.

4. Not using tally mark grouping correctly. Every group of 5 uses the diagonal cross (				) — do not write five separate vertical lines. Tally marks for 7 should be `						`, not`							`.

5. Ignoring the scale in a pictograph. Always check the key or scale before interpreting a pictograph. If one symbol equals 10 objects, then 3.5 symbols means 35 objects, not 3 or 4.

6. Unequal spacing between bars. The gaps between consecutive bars in a bar graph must be uniform. Varying the gap size misrepresents the data and makes comparison difficult.

7. Calculating mean without checking the number of observations. A common error is adding correctly but dividing by the wrong count. Always verify n (the total number of values) before dividing.

Exam Checklist

Before your exam, make sure you can do the following:

[ ] Define data, raw data, and array correctly
[ ] Organise raw data into a frequency table using tally marks
[ ] Read and interpret pictographs, including half-symbols
[ ] Draw a neat bar graph with proper title, axes, labels, and scale
[ ] Calculate the mean using the formula: Mean = Sum / n
[ ] Find the median for both odd and even numbers of observations
[ ] Identify the mode of a data set (and recognise when there is no mode)
[ ] Distinguish between mean, median, and mode for the same data set
[ ] Solve word problems involving mean, median, and mode
[ ] Identify and avoid the common mistakes listed above

Frequently Asked Questions

The science of collecting, organizing, presenting, and analyzing data.

Statistics Exercise Solutions | KalviGavani

Statistics — Exercise Solutions

How to Use This Page

Key Concepts (Quick Recap)

Data and Tally Marks

Pictographs

Bar Graphs

Mean

Median

Mode

Exercise 5.1 — Data and Tally Marks

Exercise 5.2 — Pictographs

Exercise 5.3 — Bar Graphs

Exercise 5.4 — Mean, Median, Mode

MCQs from All Exercises

Additional Questions

Common Mistakes

Exam Checklist

Frequently Asked Questions