(a) Find the mean of 7, 11, 6, 5 and 6.

(b) If each number given in (a) is diminished by 2; find the new value of mean.

(a) Sum of observations = 7 + 11 + 6 + 5 + 6 = 35.

By formula,

Mean = $\dfrac{\text{Sum of observation}}{\text{No. of observation}}$

= $\dfrac{35}{5}$ = 7.

Hence, mean = 7.

(b) We know that,

If each given number is increased or decreased by the same quantity, the value of mean is also increased or decreased by same quantity.

∴ If each number is diminished by 2, then mean will also decrease by 2.

New mean = 7 - 2 = 5.

Hence, new mean = 5.