If the mean of six observations y, y + 1, y + 4, y + 6, y + 8, y + 5 is 13, find the value of y.

We know, $\mathrm{Mean} = \frac{\mathrm{sum} \mathrm{of} \mathrm{observation}}{\mathrm{total} \mathrm{no}. \mathrm{of} \mathrm{observations}}$

=> 13 = $\frac{(\mathrm{y} + \mathrm{y} + 1+ \mathrm{y} + 4+ \mathrm{y} + 6+ \mathrm{y} + 8+ \mathrm{y} + 5) }{6}$

=> 13 = $\frac{(6\mathrm{y} + 24)}{6}$

=> (13 x 6) = 6y +24

=> (13 x 6) – 24 = 6y

=> (13 x 6) – 6 x 4 = 6y

=> 6(13 – 4) = 6y

=> y = 9