Calculate the mean, variance, and range from the given frequency distribution of haemoglobin levels for women.

Here are the calculations for Question 1:

a)
To calculate the mean, variance, and range from the frequency distribution, we first need to determine the class midpoints ($x_i$) and use the frequencies ($f_i$). The class intervals are given to the nearest 0.1 gm, so the actual class boundaries are 0.05 below the lower limit and 0.05 above the upper limit.

Let's set up the table with midpoints and other necessary calculations:

Haemoglobin Class	Class Boundaries	Midpoint ($x_i$)	Number of Women ($f_i$)	$f_i x_i$	$x_i^2$	$f_i x_i^2$
8.0 – 8.9	7.95 – 8.95	8.45	1	8.45	71.4025	71.4025
9.0 – 9.9	8.95 – 9.95	9.45	3	28.35	89.3025	267.9075
10.0 – 10.9	9.95 – 10.95	10.45	24	250.80	109.2025	2620.86
11.0 – 11.9	10.95 – 11.95	11.45	19	217.55	131.1025	2490.9475
12.0 – 12.9	11.95 – 12.95	12.45	14	174.30	155.0025	2170.035
13.0 – 13.9	12.95 – 13.95	13.45	13	174.85	180.9025	2351.7325
14.0 – 14.9	13.95 – 14.95	14.45	5	72.25	208.8025	1044.0125
15.0 – 15.9	14.95 – 15.95	15.4