Find the median of the following data (1-8)

Question 1: 83, 37, 70, 29, 45, 63, 41, 70, 34, 54

Answer:

Population size: 10

Ascending order: 29,34,37,41,45,54,63,70,70,83

Median = 49.5

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Question 2: 133, 73, 89, 108, 94, 104, 94, 85, 100, 120

Answer:

Population size: 10

Ascending order: 73,85,89,94,94,100,104,108,120,133

Median = 97

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Question 3: 31, 38, 27, 28, 36, 25, 35, 40

Answer:

Population size: 8

Ascending order: 25,27,28,31,35,36,38,40

Median = 33

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Question 4: 15, 6, 16,8, 22, 21, 9, 18, 25

Answer:

Population size: 9

Ascending order: 6,8,9,15,16,18,21,22,25

Median = 16

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Question 5: 41, 43, 127, 99, 71, 92, 71, 58, 57

Answer:

Population size: 9

Ascending order: 43,47,57,58,71,71,92,99,127

Median = 71

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Question 6: 25, 34, 31, 23, 22, 26, 35, 29, 20, 32

Answer:

Population size: 10

Ascending order: 20,22,23,25,26,29,31,32,34,35

Median = 27.5

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Question 7: 12, 17, 3, 14,5, 8, 7, 15

Answer:

Population size: 8

Ascending order: 3,5,7,8,12,14,15,17

Median = 10

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Question 8:  92, 35, 67, 85, 72, 81, 56, 51, 42, 69

Answer:

Population size: 10

Ascending order: 35,42,51,56,67,69,72,81,85,92

Median = 68

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Question 9: Numbers 50, 42, 35, 2x+10, 2x+1, 12,11, 8, 6 are written in descending order and their median is 25 , find x .

Answer:

Population size: 9

Therefore, the Median is the 5^{th} term.

Hence 2x+1 = 25 \Rightarrow 2x = 24 \Rightarrow x = 12

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Question 10: Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 . If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?

Answer:

Population size: 11

Ascending order: 33,35,41,46,55,58,64,77,87,90,92

Median = 58

If 92 is replaced by 99 and 41 by 43 Then

Population size: 11

Ascending order: 33,35,43,46,55,58,64,77,87,90,99

Median = 58

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Question 11:  Find the median of the following data 41, 43, 127, 99, 61, 92, 71, 58, 57 . If 58 is replaced by 85 , what will be the new median

Answer:

Population size: 9

Ascending order: 41,43,57,58,61,71,92,99,127

Median = 61

If 58 is replaced by 85 Then

Population size: 9

Ascending order: 41,43,57,61,71,85,92,99,127

Median = 71

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Question 12: The weights (in kg) of 15 students are: 31,35,27,29,32,43,37,41,34,28,36,44, 45, 42, 30 . Find the median. If the weight 44 \ kg is replaced by 46 \ kg and 27 \ kg by 25 \ kg , find the new median.

Answer:

Population size: 15

Ascending order: 27,28,29,30,31,32,34,35,36,37,41,42,43,44,45

Median = 35

If 58 is replaced by 85 Then

Population size: 15

Ascending order: 25,28,29,30,31,32,34,35,36,37,41,42,43,45,46

Median = 35

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Question 13: The following observations have been arranged in ascending order. If the median of the data is 63 , find the value of x: 29,32, 48,50,x, x+2,72,78, 84,95

Answer:

Population Size: 10

Therefore \frac{x + (x+2)}{2} = 63

\Rightarrow 2x + 2 = 126 \Rightarrow x = 62

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Question 14: If the mean of the observations 45, 52, 60 x, 69,70,76, 81, 94 is 68 , find its median.

Answer:

Mean:  68 = \frac{45+52+60+x+69+70+76+81+94}{9}

\Rightarrow 612 = 547+x

\Rightarrow x = 65

Population Size: 9

Therefore Median is the 5^{th} term

Hence Median is 69

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Question 15: The numbers 6,8,10,12,13 and x are arranged in ascending order. If the mean of these observations is equal to the median find the value of x .

Answer:

Population size: 6

Median = \frac{10+12}{2} = 11

Therefore 11 = \frac{6+8+10+12+13+x}{6} 

\Rightarrow 66 = 49 + x

\Rightarrow x = 17

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Question 16: The median of the following observations : 11, 12, 14, (x - 2), (x + 4) , (x + 9), 32, 38,47 arranged in ascending order is 24 . Find the value of x and hence find the median.

Answer:

Population size: 9

Median = (x+4)

Therefore x+4 = 24 \Rightarrow x = 20

Mean = \frac{11+ 12+ 14+ (20 - 2)+(20 + 4)+(20 + 9)+32+38+47}{9} = 25

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Question 17: If the mean of observations : 8, 10, 7, 6, 10, x, 6, 13, 10 is 9 , find the median.

Answer:

Mean:  9 = \frac{8+10+7+6+10+x+6+13+10}{9}

\Rightarrow 81 = 70+x

\Rightarrow x = 11

Population Size: 9

Ascending order: 6,6,7,8,10,10,10,11,13

Therefore Median is the 5^{th} term

Hence Median is 10

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