Class 6: Maths Chapter 34 solutions. Complete Class 6 Maths Chapter 34 Notes.
Selina Class 6 ICSE Solutions Mathematics : Chapter 34- Mean and Median
Selina 6th Maths Chapter 34, Class 6 Maths Chapter 34 solutions
Exercise 34(A)
1. Find the mean of:
(i) 7, 10, 4 and 17
(ii) 12, 9, 6, 11 and 17
(iii) 3, 1, 5, 4, 4 and 7
(iv) 7, 5, 0, 3, 0, 6, 0, 9, 1 and 4
(v) 2.1, 4.5, 5.2, 7.1 and 9.3
Solution:
(i) Given
Numbers are 7, 10, 4 and 17
The mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (7 + 10 + 4 + 17) / 4
We get,
= 38 / 4
= 9.5
Hence, mean = 9.5
(ii) Given
Numbers are 12, 9, 6, 11 and 17
The mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (12 + 9 + 6 + 11 + 17) / 5
We get,
= 55 / 5
= 11
Hence, mean = 11
(iii) Given
Numbers are 3, 1, 5, 4, 4 and 7
The mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (3 + 1 + 5 + 4 + 4 + 7) / 6
We get,
= 24 / 6
= 4
Hence, mean = 4
(iv) Given
Numbers are 7, 5, 0, 3, 0, 6, 0, 9, 1 and 4
The mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (7 + 5 + 0 + 3 + 0 + 6 + 0 + 9 + 1 + 4) / 10
We get,
= 35 / 10
= 3.5
Hence, mean = 3.5
(v) Given
Numbers are 2.1, 4.5, 5.2, 7.1 and 9.3
The mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (2.1 + 4.5 + 5.2 + 7.1 + 9.3) / 5
We get,
= 28.2 / 5
= 5.64
Hence, mean = 5.64
2. Find the mean of:
(i) first eight natural numbers
(ii) first six even natural numbers
(iii) first five odd natural numbers
(iv) all prime numbers upto 30
(v) all prime numbers between 20 and 40
Solution:
(i) The first eight natural numbers are as follows:
1, 2, 3, 4, 5, 6, 7 and 8
Hence, the mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8
We get,
= 36 / 8
= 4.5
Therefore, mean = 4.5
(ii) The first six even natural numbers are as follows:
2, 4, 6, 8, 10 and 12
Hence, the mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (2 + 4 + 6 + 8 + 10 + 12) / 6
We get,
= 42 / 6
= 7
Therefore, mean = 7
(iii) First five odd natural numbers are as follows:
1, 3, 5, 7 and 9
Hence, the mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (1 + 3 + 5 + 7 + 9) / 5
We get,
= 25 / 5
= 5
Therefore, mean = 5
(iv) Prime numbers till 30 are as follows:
2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
Hence, the mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29) / 10
We get,
= 129 / 10
= 12.9
Therefore, mean = 12.9
(v) All prime numbers between 20 and 40 are as follows:
23, 29, 31 and 37
Hence, the mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (23 + 29 + 31 + 37) / 4
We get,
= 120 / 4
= 30
Therefore, mean = 30
3. Height (in cm) of 7 boys of a locality are 144 cm, 155 cm, 168 cm, 163 cm, 167 cm, 151 cm and 158 cm. Find their mean height.
Solution:
Given
Height of 7 boys of a locality = 144 cm, 155 cm, 168 cm, 163 cm, 167 cm, 151 cm and 158 cm
Hence, the mean can be calculated as follows:
Mean = Sum of height / Number of boys
= (144 + 155 + 168 + 163 + 167 + 151 + 158) / 7
We get,
= 1106 / 7
= 158 cm
Therefore, mean height = 158 cm
4. Find the mean of 35, 44, 31, 57, 38, 29, 26, 36, 41 and 43.
Solution:
Given
Numbers are 35, 44, 31, 57, 38, 29, 26, 36, 41 and 43
Hence, the mean can be calculated as below
Mean = Sum of numbers / Number of numbers
= (35 + 44 + 31 + 57 + 38 + 29 + 26 + 36 + 41 + 43) / 10
We get,
= 380 / 10
= 38
Therefore, mean = 38
5. The mean of 18, 28, x, 32, 14 and 36 is 23. Find the value of x. Sum of data
Solution:
Given
Mean of 18, 28, x, 32, 14 and 36 = 23
Hence, the value of x can be calculated as below
Mean = (Sum of numbers) / (Number of numbers)
23 = (18 + 28 + x + 32 + 14 + 36) / 6
On further calculation, we get
23 × 6 = x + 128
138 = x + 128
x = 138 – 128
We get,
x = 10
Hence, the value of x is 10
6. If the mean of x, x + 2, x + 4, x + 6 and x + 8 is13, find the value of x. Sum of data
Solution:
Given
Mean of x, x + 2, x + 4, x + 6 and x + 8 is 13
Hence, the value of x can be calculated as below
Mean = (Sum of numbers) / (Number of numbers)
13 = [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)] / 5
On further calculation, we get
13 × 5 = 5x + 20
65 = 5x + 20
5x = 65 – 20
5x = 45
We get,
x = 9
Hence, the value of x is 9
Exercise 34(B)
1. Find the median of
(i) 21, 21, 22, 23, 23, 24, 24, 24, 24, 25 and 25
(ii) 3.2, 4.8, 5.6, 5.6, 7.3, 8.9 and 91
(iii) 17, 23, 36, 12, 18, 23, 40 and 20
(iv) 26, 33, 41, 18, 30, 22, 36, 45 and 24
(v) 80, 48, 66, 61, 75, 52, 45 and 70
Solution:
(i) Given
Numbers are 21, 21, 22, 23, 23, 24, 24, 24, 24, 25 and 25
Total numbers = 11
Total number of numbers is odd
Hence, the median will be the middle number
Here, middle number is 24
Therefore, the median is 24
(ii) Given
Numbers are 3.2, 4.8, 5.6, 5.6, 7.3, 8.9 and 91
Total numbers = 7
Total number of numbers is odd
Hence, the median will be the middle number
Here, middle number is 5.6
Therefore, the median is 5.6
(iii) Given
Numbers are 17, 23, 36, 12, 18, 23, 40 and 20
Total numbers = 8
Total number of numbers is even
Hence, the median will be the half of the sum of two middle numbers
So, the median can be calculated as below
Median = (Sum of two middle numbers) / 2
= (12 + 18) / 2
= 30 / 2
We get,
= 15
Therefore, the median is 15
(iv) Given
Numbers are 26, 33, 41, 18, 30, 22, 36, 45 and 24
Total numbers = 9
Here, total number of numbers is odd
Hence, the median will be the middle number
Here, the middle number is 30
Therefore, the median is 30
(v) Given
Numbers are 80, 48, 66, 61, 75, 52, 45 and 70
Total numbers = 8
Total number of numbers is even
Hence, the median will be the half of the sum of the two middle numbers
So, the median can be calculated as below
Median = (Sum of two middle numbers) / 2
= (61 + 75) / 2
= 136 / 2
We get,
= 68
Therefore, the median is 68
2. Find the mean and the median of:
(i) 1, 3, 4, 5, 9, 9 and 11
(ii) 10, 12, 12, 15, 15, 17, 18, 18, 18 and 19
(iii) 2, 4, 5, 8, 10, 13 and 14
(iv) 5, 8, 10, 11, 13, 16, 19 and 20
(v) 1.2, 1.9, 2.2, 2.6 and 2.9
Solution:
(i) Given
Numbers are 1, 3, 4, 5, 9, 9 and 11
Hence, the mean can be calculated as below
Mean = (Sum of numbers) / (Number of numbers)
= (1 + 3 + 4 + 5 + 9 + 9 + 11) / 7
= 42 / 7
We get,
= 6
Hence, the mean is 6
Total numbers are 7
Since, total number of numbers is odd
Therefore, the median will be the middle number
Here, middle number is 5
Therefore, the median is 5
(ii) Given
Numbers are 10, 12, 12, 15, 15, 17, 18, 18, 18 and 19
The mean can be calculated as below
Mean = (Sum of numbers) / (Number of numbers)
= (10 + 12 + 12 + 15 + 15 + 17 + 18 + 18 + 18 + 19) / 10
= 154 / 10
We get,
= 15.4
Hence, mean is 15.4
Total numbers are 10
Since, total number of numbers is even
Therefore, the median will be the half of the sum of two middle numbers
The median can be calculated as below
Median = (Sum of two middle numbers) / 2
= (15 + 17) / 2
= 32 / 2
We get,
= 16
Therefore, the median is 16
(iii) Given
Numbers are 2, 4, 5, 8, 10, 13 and 14
The mean can be calculated as below
Mean = (Sum of numbers) / (Number of numbers)
= (2 + 4 + 5 + 8 + 10 + 13 + 14) / 7
= 56 / 7
We get,
= 8
Hence, mean is 8
Total numbers are 7
Since, total number of numbers is odd
Therefore, the median will be the middle number
Here, middle number is 8
Therefore, the median is 8
(iv) Given
Numbers are 5, 8, 10, 11, 13, 16, 19 and 20
The mean can be calculated as below
Mean = (Sum of numbers) / (Number of numbers)
= (5 + 8 + 10 + 11 + 13 + 16 + 19 + 20) / 8
= 102 / 8
We get,
= 12.75
Hence, mean is 12.75
Total numbers are 8
Since, total number of numbers is even
Therefore, the median will be the half of the sum of two middle numbers
The median can be calculated as below
Median = (Sum of two middle numbers) / 2
= (11 + 13) / 2
= 24 / 2
We get,
= 12
Therefore, the median is 12
(v) Given
Numbers are 1.2, 1.9, 2.2, 2.6 and 2.9
The mean can be calculated as below
Mean = (Sum of numbers) / (Number of numbers)
= (1.2 + 1.9 + 2.2 + 2.6 + 2.9) / 5
= 10.8 / 5
We get,
= 2.16
Hence, the mean is 2.16
Total numbers are 5
Since, total number of numbers is odd
Therefore, the median will be the middle number
Here, middle number is 2.2
Therefore, the median is 2.2
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Selina Class 6 ICSE Solutions Mathematics : Chapter 34- Mean and Median
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Chapterwise Selina Publishers ICSE Solutions for Class 6 Mathematics :
- Chapter 1- Number System
- Chapter 2- Estimation
- Chapter 3- Numbers In Indian And International Systems
- Chapter 4- Place Value
- Chapter 5- Natural Numbers And Whole Numbers
- Chapter 6- Negative Numbers And Integers
- Chapter 7- Number Line
- Chapter 8- HCF And LCM
- Chapter 9- Playing With Numbers
- Chapter 10- Sets
- Chapter 11- Ratio
- Chapter 12- Proportion
- Chapter 13- Unitary Method
- Chapter 14- Fractions
- Chapter 15- Decimal Fractions
- Chapter 16- Percent (Percentage)
- Chapter 17- Idea of Speed, Distance and Time
- Chapter 18- Fundamental Concepts
- Chapter 19- Fundamental Operations
- Chapter 20- Substitution
- Chapter 21- Framing Algebraic Expressions (Including Evaluation)
- Chapter 22- Simple (Linear) Equations
- Chapter 23- Fundamental Concepts
- Chapter 24- Angles
- Chapter 25- Properties of Angles and Lines
- Chapter 26- Triangles
- Chapter 27- Quadrilateral
- Chapter 28- Polygons
- Chapter 29- The Circle
- Chapter 30- Revision Exercise Symmetry
- Chapter 31- Recognition of Solids
- Chapter 32- Perimeter and Area of Plane Figures
- Chapter 33- Data Handling
- Chapter 34- Mean and Median
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