The following table illustrates the heights, in centimetres, of 150 children.

Height (cm) ......................    No. children ( f )
140 up to 144 .................................... a
144 up to 150 .................................... b
150 up to 160 .................................. 69
160 up to 165 .................................. 28

a. Given that a calculated estimate of the mean height is exactly 153.14 cm, show that 142a +147b = 7726, and evaluate a and b.

b. Calculate an estimate of the standard deviation of the heights.