Mathematics Theory Class Interval Frequency 60 – 64 2 65 – 69 3 70 – 74 6…

Class Interval	Frequency
60 – 64	2
65 – 69	3
70 – 74	6
75 – 79	11
80 – 84	8
85 – 89	7
90 – 94	2
95 – 99	1

The table shows the distribution of marks scored by students in an examination. Calculate, correct to 2 decimal places, the

(a) mean ; (b) standard deviation of the distribution.

Explanation

Class Interval	Freq (f)	Mid-point (x)	(fx)	(x^{2})	(fx^{2})
60 – 64	2	62	124	3844	7688
65 – 69	3	67	201	4489	13487
70 – 74	6	72	432	5184	31104
75 – 79	11	77	847	5929	65219
80 – 84	8	82	656	6724	53792
85 – 89	7	87	609	7569	52983
90 – 94	2	92	184	8464	16928
95 – 99	1	97	97	9409	9409
(sum)	40		3150		250590

(a) Mean (bar{x} = frac{sum fx}{sum f})

= (frac{3150}{40})

= 78.75

(b) (SD = sqrt{frac{sum fx^{2}}{sum f} – (frac{sum fx}{sum f})^{2}})

= (sqrt{frac{250590}{40} – (frac{3150}{40})^{2}})

= (sqrt{6264.75 – (78.75)^{2}})

= (sqrt{6264.75 – 6201.5625})

= (sqrt{63.1875})

= 7.95.