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# The Numbers 6, 8, 10, 12, 13 and X Are Arranged in an Ascending Order. If the Mean of the Observations is Equal to the Median, Find the Value of X - ICSE Class 10 - Mathematics

#### Question

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

#### Solution

Given data in ascending order: 6, 8, 10, 12, 13, x

Total number of observation = N = 6 (even)

:. Median = ((N/2)^"th" term + (N/2 +1)^"th" term)/2

= ((6/2)^"th" term + (6/2 + 1)^"th" term)/2

= ("3 rd term +  4th term")/2

= (10 + 12)/2

= 22/2

= 11

Now, Mean = (6 + 8 + 10 + 12 + 13 + x)/6 = (49 + x)/6

It is given that

Mean = Median

=> (49 + x)/6 = 11

=> 49 + x = 66

=> x = 17

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#### APPEARS IN

2013-2014 (March) (with solutions)
Question 4.1 | 3.00 marks

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Solution The Numbers 6, 8, 10, 12, 13 and X Are Arranged in an Ascending Order. If the Mean of the Observations is Equal to the Median, Find the Value of X Concept: Median of Grouped Data.
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