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.

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The table shows the distribution of marks scored by students in an examination. ...

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ClassInterval	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

ClassInterval	Freq(f)	Mid-point(x)	$f x$	$x^{2}$	$f x^{2}$
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 f x}{\sum f}

\frac{3150}{40}

= 78.75
(b)

S D = \sqrt{\frac{\sum f x^{2}}{\sum f} - (\frac{\sum f x}{\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.

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