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-

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 .