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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
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.
Source: Myschool Past Questions Archive (Record #52718)