If the median of data:56,58,63,x-5,x+1,75,81,85is67,then find the value of x and also find its mean.
Answers 2
Step-by-step explanation:
We know that,
Median = 1/2 [n/2th term +( n/2+1 th term ]
Here,
n=8 which is even
Therefore,
Median = 1/2 [4 th term + 5 th term]
67 =1/2(x-5+x+1)
67=2x-4/2
2x-4=67(2)
2x=134+4
2x=138
x=138/2
x=69
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Author:
nathanialyzxw
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Given,
Series: 56,58,63,x-5,x+1,75,81,85
Median = 67
To Find,
Value of x =?
Mean =?
Solution,
Median for even number of observations,
Median = [(n/2)th observation + ( (n+1)/2)th observation] / 2
Median = (4th observation + 5th observation)/2
Meadian = 67 = (x - 5 +x + 1)/2
67 = (2x - 4)/2
67 * 2 = 2x - 4
134 + 4 = 2x
2x = 138
x = 138/2
x = 69
4th observation = 69 - 5 = 64
5th observation = 69 + 1 = 70
We know that mean is the sum of all observations divided by the total number of observations.
Mean = sum of all observation / Total Observations
Mean = (56 + 58 + 63 + 64 + 70 + 75 + 81 + 85)/8
Mean = 552/8
Mean = 69
Hence, the value of x and mean of the series are 69 and 69 respectively.
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Author:
blackjackgraham
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