If 6, 8, 10, 12, 13, x are in increasing order and their mean and median are equal, then find the value of x.
WBBSE
Class X
Mathematics
Statistics
02 Mark
2023
Numbers in ascending order are 6, 8, 10, 12, 13, x
Mean = 6 + 8 + 10 + 12 + 13 + x\over 6 = 49 + x\over 6
No. of terms (n) (even)
Median = {\text{n}\over2} \text{term} +{\text{n}\over2} + 1 \text{term}\over 2Â
= {6\over2} \text{term} +({6\over2} + 1) \text{term}\over 2Â
= 3^{rd} \text{term} +4^{th} \text{term}\over 2Â
= 10 + 12\over 2Â = 11
ATP: Mean = Median
or, 49 + \text{x}\over 6 = 11
or, x = 17
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