The marks scored by 50 students in a Geography examination are as follows : 60 54 40 67 53 73 37 55 62 43 44 69 39 32 45 58 48 67 39 51 46 59 40 52 61 48 23...
Question 1 Report
The marks scored by 50 students in a Geography examination are as follows :
60 54 40 67 53 73 37 55 62 43 44 69 39 32 45 58 48 67 39 51 46 59 40 52 61 48 23 60 59 47 65 58 74 47 40 59 68 51 50 50 71 51 26 36 38 70 46 40 51 42.
(a) Using class intervals 21 - 30, 31 - 40, ..., prepare a frequency distribution table.
(b) Calculate the mean mark of the distribution.
(c) What percentage of the students scored more than 60%?
Answer Details
(a) Frequency distribution table
| Class interval | Frequency \(f\) | Midpoint \(x\) | \(fx\) |
|---|---|---|---|
| 21 - 30 | 2 | 25.5 | 51.0 |
| 31 - 40 | 10 | 35.5 | 355.0 |
| 41 - 50 | 12 | 45.5 | 546.0 |
| 51 - 60 | 15 | 55.5 | 832.5 |
| 61 - 70 | 8 | 65.5 | 524.0 |
| 71 - 80 | 3 | 75.5 | 226.5 |
| Total | 50 | 2535.0 |
(b) Mean \[\bar{x} = \frac{\sum fx}{\sum f} = \frac{2535}{50} = \mathbf{50.7}.\]
(c) Marks more than \(60\): the values greater than \(60\) are \(61, 62, 65, 67, 67, 68, 69, 70, 71, 73, 74\) - that is \(11\) students. \[\text{percentage} = \frac{11}{50}\times 100 = \mathbf{22\%}.\]
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