The mean of following numbers is $68$ . Find the value of $x$ .
$45, 52, 60, x, 69, 70, 26, 81$ and $94$ .
Hence estimate the median.

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Solution

$M e a n = \frac{Sum of variates}{Number of variates}$

$68 = \frac{45 + 52 + 60 + x + 69 + 70 + 26 + 81 + 94}{9}$
$612 = 497 + x$
$115 = x$
On arranging the given numbers in ascending order, we get
$26, 45, 52, 60, 69, 70, 81, 94, 115$
No. of terms $(n) = 9 (o d d)$
$M e d i a n =$ Value of ${(\frac{n + 1}{2})}^{t h}$ term
$=$ Value of ${(\frac{9 + 1}{2})}^{t h} t e r m$
$= 5 t h t e r m$
$= 69$

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The mean of following numbers is 68. Find the value of x.45,52,60,x,69,70,26,81 and 94.Hence estimate the median.

Mean=Sum of variatesNumber of variates68=45+52+60+x+69+70+26+81+949612=497+x115=xOn arranging the given numbers in ascending order, we get26,45,52,60,69,70,81,94,115No. of terms (n)=9(odd)Median= Value of (n+12)th term= Value of (9+12)thterm=5th term=69

The mean of following numbers is $68$ . Find the value of $x$ .
$45, 52, 60, x, 69, 70, 26, 81$ and $94$ .
Hence estimate the median.