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 b...
Question 1 Report
| 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.
Answer Details
Working table (midpoint \(x\), \(N = 40\)).
| Class | x | f | fx | fx² |
|---|---|---|---|---|
| 60-64 | 62 | 2 | 124 | 7688 |
| 65-69 | 67 | 3 | 201 | 13467 |
| 70-74 | 72 | 6 | 432 | 31104 |
| 75-79 | 77 | 11 | 847 | 65219 |
| 80-84 | 82 | 8 | 656 | 53792 |
| 85-89 | 87 | 7 | 609 | 52983 |
| 90-94 | 92 | 2 | 184 | 16928 |
| 95-99 | 97 | 1 | 97 | 9409 |
| Total | 40 | 3150 | 250590 |
(a) Mean.
\[\bar{x} = \frac{\sum fx}{\sum f} = \frac{3150}{40} = \mathbf{78.75}\](b) Standard deviation.
\[\sigma = \sqrt{\frac{\sum fx^{2}}{N} - \bar{x}^{2}} = \sqrt{\frac{250590}{40} - 78.75^{2}}\] \[= \sqrt{6264.75 - 6201.5625} = \sqrt{63.1875} = \mathbf{7.95}\]Download The App On Google Playstore
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