The mean,median and mode of the data values 90,54,x,123,62,78,58,81 are all equal. What is the value of x?


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Question Number 111533 by Aina Samuel Temidayo last updated on 04/Sep/20

$The mean, median and mode of the$ $data values 90, 54, x, 123, 62, 78, 58, 81$ $are all equal . What is the value of x ?$
Commented by Rasheed.Sindhi last updated on 04/Sep/20

$78$
Commented by Aina Samuel Temidayo last updated on 04/Sep/20

$Your solution please ?$
	Answered by Rasheed.Sindhi last updated on 05/Sep/20

	$I f x h a s a v a l u e o t h e r t h a n$ $90, 54, 123, 62, 78, 58, 81 t h e n t h e$ $m o d e {d o e s n}^{'} t e x i s t .$ $B u t a s t h e m o d e e x i s t s s o$ $x \in {90, 54, 123, 62, 78, 58, 81}$ $A n d a l s o m o d e i s x (∵ i t e x i s t$ $t w i c e a n d a l l o t h e r s o n c e o n l y)$ $N o w$ $m e a n = m o d e$ $\frac{90 + 54 + x + 123 + 62 + 78 + 58 + 81}{8} = x$ $546 + x = 8 x$ $x = 78$ $F o r t u n a t e l y {i t}^{'} s a l s o m e d i a n$ $123, 90, 81, 78, 78, 62, 58, 54$ $M i d d l e p o s i t i o n n u m b e r s : 78, 78$ $S o, m e d i a n = \frac{78 + 78}{2} = 78$ $F i n a l l y,$ $x = m e a n = m o d e = m e d i a n = 78$
	Commented by Aina Samuel Temidayo last updated on 05/Sep/20

	$Thanks .$
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