Class 6

Samacheer Kalvi 6th Tamil Book Answers Solutions Guide

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Samacheer Kalvi 6th Books Solutions Guide

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Samacheer Kalvi 6th Maths Book Answers Solutions Guide

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Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 6 Information Processing Ex 6.2

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Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 6 Information Processing Ex 6.2

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 6 Information Processing Ex 6.2

Question 1.
In the following magic triangle, arrange the numbers from 1 to 6, so that you get the same sum on all its sides.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q1
Solution:
Step 1: Complete the corners with smaller numbers 1, 2 and 3.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q1.1
Step 2: The side having smallest numbers 1 & 2 are to be filled with the greatest number 6, the second smallest 1 & 3 side to be filled with the second largest 5 at the middle and so on.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q1.2
The magic sum is 1 + 6 + 2 = 2 + 4 + 3 = 3 + 5 + 1 = 9. Some other ways are given below.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q1.3
The magic sum = 1 + 6 + 3 = 3 + 2 + 5 = 5 + 4 + 1 = 10.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q1.4
The magic sum 6 + 1 + 4 = 4 + 5 + 2 = 2 + 3 + 6 = 11.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q1.5
The magic sum 4 + 3 + 5 = 5 + 1 + 6 = 6 + 2 + 4 = 12.

Question 2.
Using the numbers from 1 to 9
(i) Can you form a magic triangle?
(ii) How many magic triangles can be formed?
(iii) What are the sums of the sides of the magic triangle?
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q2
Solution:
(i) Yes, we can form
(ii) 5
(iii)
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q2.1
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q2.2
Sums are 17, 19, 20, 21, and 23.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 6 Information Processing Ex 6.2

Question 3.
Arrange the odd numbers from 1 to 17 without repetition to get a sum of 30 on each side of the magic triangle.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q3
Solution:
The odd numbers between 1 to 17 are 1, 3, 5, 7, 9, 11, 13, 15, 17.
Step 1: Place the smaller numbers 1, 3, 5 on the comers.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q3.1
Step 2: Arrange another set of smaller numbers 7, 9, and 11 on each side.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q3.2
Step 3: Arrange the remaining numbers 13,15,17 to give the total 30.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q3.3
Magic sum = 30.

Question 4.
Put the numbers 1, 2, 3, 4, 5, 6, and 7 in the circles so that each straight line of three numbers add up to the same total.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q4
Solution:
Here there is even number of terms. Also we know that 1 + 6 = 7, 2 + 5 = 7, 3 + 4 = 7; so placing 7 at the centre, and the pairs (1, 6) (2, 5) and (3, 4) at. the opposite ends we get, the answer.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q4.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 6 Information Processing Ex 6.2

Question 5.
Place the number 1 to 12 in the 12 circles so that the sum of the numbers in each of the six lines of the star is 26. Use each number from 1 to 12 exactly once. Find more possible ways.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q5
Solution:
The given star can be viewed as two magical triangular as.
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q5.1
Now the required arrangement is
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q5.2
Some other arrangements are
Samacheer Kalvi 6th Maths Term 1 Chapter 6 Information Processing Ex 6.2 Q5.3

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.4

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Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.4

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Miscellaneous Practice Problems

Question 1.
The heights (in centimetres) of 40 children are
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q1
Prepare a tally mark table.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q1.1

Question 2.
There are 1000 students in a school. Data regarding the mode of transport of the students as given below. Draw a pictograph to represent the data.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q2
Solution:
The pictograph for the mode of transport of students.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q2.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.4

Question 3.
The following pictograph shows the total savings of a group of friends in a year. Each picture represents a saving of Rs. 100. Answer the following questions.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q3
(i) What is the ratio of Ruby’s saving to that of Thasnim’s?
(ii) What is the ratio of Kuzhali’s savings to that of others?
(iii) How much is Iniya’s savings?
(iv) Find the total amount of savings of all your friends?
(v) Ruby and Kuzhali save the same amount. Say True or False.
Solution:
(i) Ratio of Ruby’s saving to that of Thasnim’s
\(=\frac{\text { Ruby’s saving }}{\text { Thasnim’s saving }}=\frac{5 \times 100}{4 \times 100}=\frac{5}{4}=5: 4\)
Ratio of Ruby’s saving to that of Thasnims = 5 : 4
(ii) Ratio of Kuzhali’s savings to that of others
\(=\frac{\text { kuzhali’s saving }}{\text { others saving }}=\frac{5 \times 100}{19 \times 100}=\frac{5}{19}=5: 19\)
Ratio of Kuzhali’s saving to that of others = 5 : 19
(iii) Iniya’s saving = 3 × 100 = ₹ 300
(iv) Saving of all the friends = (5 + 7 + 4 + 5 + 3) × 100 = 24 × 100 = ₹ 2400.
Total savings = ₹ 2400
(v) True.

Challenging Problems

Question 4.
The table shows the number of moons that orbit each of the planets in our solar system.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q4
Make a Bar graph for the above data.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q4.1

Question 5.
The predictions of Weather in the month of September is given below:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q5
(i) Make a frequency table of the types of weather by reading the calender.
(ii) How many days are either cloudy or partly cloudy
(iii) How many days do not have rain? Give two ways to find the answer?
(iv) Find the ratio of the number of sunny days to Rainy days.
Solution:
Frequency Table for the Type of weather for the month of September
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q5.1
(ii) 14 days.
(iii) For 24 days there is no rain.
(a) From the total 30 days, we subtract the rainy days i.e 30 – 6 = 24 days (from the frequency table)
(b) From the picture, we can count the non-rainy days.
(iv) Ratio of number of Sunny day to Rainy days
\(=\frac{\text { Number of Sunny days }}{\text { Number of Rainy days }}=\frac{10}{6}=\frac{5}{3}=5: 3\)
The ratio of a number of Sunny days to Rainy days = 5 : 3.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.4

Question 6.
26 students were interviewed to find out what they want to become in the future. Their responses are given in the following table.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q6
Represent this data using the pictograph
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q6.1

Question 7.
Yasmin of class VI was given a task to count the number of books which are biographies, in her school library. The information collected by her is represented as follows.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q7
Observe the pictograph and answer the following questions.
(i) Which title has the maximum number of biographies?
(ii) Which title has the minimum number of biographies?
(iii) Which title has exactly half the number of biographies as Novelists?
(iv) How many biographies are there on the title of Sportspersons?
(v) What is the total number of biographies in the library?
Solution:
(i) ‘The title Novelists’ have the maximum number of biographies
(ii) ‘The title Scientists’ have a minimum number of biographies.
(iii) ‘Sportspersons’ title has exactly half the number of biographies as Novelist.
(iv) \((1 \times 20)+\frac{20}{4}=20+5=25\) biographies are there in the title sportsperson.
(v) 8 × 20 = 160 biographies are there in the library.

Question 8.
The bar graph illustrates the results of a survey conducted on vehicles crossing over a Toll Plaza in one hour.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q8
Observe the bar graph carefully and fill up the following table.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q8.1
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q8.2

Question 9.
The lengths (in the nearest centimetre) of 30 drumsticks are given as follows.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q9
Draw the bar graph showing the same information.
Solution:
The bar graph showing the same information is given below:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q9.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.4

Question 10.
Given two angles are supplementary i.e. their sum = 180°.
Solution:
Let the angle be x.
Then anothcf angle = x + 20 (given)
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.4 Q10
The two angles are 80° and 100°

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Intext Questions

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Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Intext Questions

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Intext Questions

Recap (Textbook Page No. 108)

Question 1.
Count the objects in the following figure and complete the table that follows :
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Intext Questions Q1
From Fig 5.1 and the table, answer the following question.
(i) The total number of objects in the above picture is ______
(ii) The difference between the number of squares and the number of bats is ______
(iii) The ratio of the number of balls to the number of bats is _______
(iv) What are the objects equal in number?
(v) How many more balls are there than the number of bats?
Solution:
(i) 24
(ii) 0
(iii) \(\frac{8}{6}=\frac{4}{3}\)
(iv) Bat and Square
(v) 2 balls more
Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Intext Questions

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Additional Questions

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Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Additional Questions

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Additional Questions

Question 1.
A _____ is a collection of numbers gathered to give some meaningful information.
Solution:
Data

Question 2.
The data can be arranged in a tabular form using ____ marks
Solution:
Tally

Question 3.
A observation occurring 8 times in a data is represented as _____ using tally marks.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 1 Q3

Question 4.
Tally marks Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 1 Q4 represents _____
Solution:
6

Question 5.
Following are the choice of sports for 20 students of class VI.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 1 Q5
Arrange the names of sports in a table using tally marks.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 1 Q5.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Additional Questions

Question 6.
Mariana threw a die 40 times and noted the number appearing each time as shown below.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 1 Q6
Make a table and enter the data using tally marks.
Find the number that appeared
(a) the minimum number of times
(b) the maximum number of times
(c) Find those numbers that appear an equal number of times.
Solution:
Table using Tally Marks
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 1 Q6.1
(a) The number ‘4’ appeared the minimum number of times
(b) The number ‘5’ appeared the maximum number of times
(c) Numbers ‘1’ and ‘6’ appeared the equal number of times.

Question 7.
What is the advantage of using pictograph?
Solution:
The data can be analyzed and interpreted. The pictures and symbols help us to understand better.

Question 8.
Total number of students of a school in different years is shown in the following table
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 2 Q1
(A) Prepare a pictograph of students using one symbol to represent 100 students and answer the following questions
(a) How many symbols represent the total number of students in the year 2000?
(b) How many symbols represent the total number of students in the year 1997?
Solution:
(A) The pictograph is given by
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 2 Q1.1
(a) 9 Full pictures and a half picture represent the number of students in the year 2000
(b) 5 symbols.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Additional Questions

Question 9.
The number of bottles of honey sold by three different shops are given below.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 2 Q2
(A) Draw a pictograph and answer the following questions (use the scale – 20 bottles)
(a) What is the total profit of shop A, if the profit gained on each bottle is ‘E’150?
(b) If the total number of bottles sold is 400 how many figures must be drawn to shops?
(c) Find the difference between the number of bottles sold by shop B and the number of bottles sold by shop ‘C’.
Solution:
(A) Pictograph of number of bottles sold
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 2 Q2.1
(a) Profit per bottle = ₹ 150
Shop A’s total profit = 80 × 150 = ₹ 12,000
(b) For 400 bottles, the figures to be drawn is \(\frac{400}{20}\) = 20 bottles for shop ‘C ’
(c) Difference = No. of bottles sold by shop ‘C’ – No. of bottles sold by shop ‘B’ = 180 – 140 = 40 bottles

Question 10.
The following data is the total savings of a group of 5 friends in a year.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 3 Q1
Draw a pictograph to represent the data.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 3 Q1.1

Question 11.
The number of mathematics books sold by a shopkeeper on six consecutive days is shown below.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 3 Q2
Draw a bar graph to represent the above information choosing the scale of your choice.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 3 Q2.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Additional Questions

Question 12.
The following bar graph shows the number of people visited Mahabalipuram over a period of 5 months.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Additional Questions 3 Q3
Use the graph to answer the following questions
(a) How many people visited Mahabalipuram in April?
(b) How many more people visited Mahabalipuram in May than in January?
(c) In which month, were there as many visitors as in March?
(d) In which month was there 1500 more visitors than in January?
(e) How many visitors were there in 5 months?
Solution:
(a) 3500 people visited Mahabalipuram in April
(b) 500 more people
(c) January
(d) April
(e) 11,500 people

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Additional Questions