Question

The following are marks scored by form four student in Mathematics test.

Marks	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89	90-99
Frequency	2	6	10	16	24	20	12	8	2

Using an assumed mean of 54.5, calculate the

1. Mean mark 
2. Variance 
3. Standard deviation 

Answer 1

1. Mean mark 

   Marks	Mp(x)	d(x-a)	Fd	D2	Fd2
   10-19	2	14.5	-40	-80	1600	3200
   20-29	6	24.5	-30	-180	900	5400
   30-39	10	34.5	-20	-200	400	4000
   40-49	16	44.5	-10	-160	100	1600
   50-59	24	54.5	0	0	0	0
   60-69	20	64.5	10	200	100	200
   70-79	12	74.5	20	240	400	4800
   80-89	8	84.5	30	240	900	7200
   90-99	2	94.5	40	80	1600	3200
   				140		31400

2. Mean = A + Σfd
                   Σf
   = 54.5 + 140/100 = 55.9
3. Variance 
   Variance= 31400/100 – (140/100)²
   = 312.04
4. Standard deviation 
   standard variation = √variance
   √ 312.04 = 17.06