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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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