Marks obtained (in mathematics) by 9 students are given below :

60, 67, 52, 76, 50, 51, 74, 45 and 56.

(a) Find the arithmetic mean.

(b) If marks of each student be increased by 4; what will be the new value of arithmetic mean?

(a) Sum of observations = 60 + 67 + 52 + 76 + 50 + 51 + 74 + 45 + 56 = 531.

By formula,

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

= $\dfrac{531}{9}$ = 59.

Hence, mean = 59.

(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 marks of each student is increased by 4, then mean will also increase by 4.

New mean = 59 + 4 = 63.

Hence, new mean = 63.