The marks obtained by 40 students in an examination are as follows :
85 77 87 74 77 78 79 89 95 90 78 73 86 83 91 74 84 81 83 75 77 70 81 69 75 63 76 87 61 78 69 96 65 80 84 80 77 74 88 72.
(a) Copy and complete the table for the distribution using the above data.
(b) Draw a histogram to represent the distribution.
(c) Using your histogram, estimate the modal mark.
(d) If a student is chosen at random, find the probability that the student obtains a mark greater than 79.
85 77 87 74 77 78 79 89 95 90 78 73 86 83 91 74 84 81 83 75 77 70 81 69 75 63 76 87 61 78 69 96 65 80 84 80 77 74 88 72.
(a) Copy and complete the table for the distribution using the above data.
| Class Boundaries | Tally | Frequency |
| 59.5 - 64.5 | ||
| 64.5 - 69.5 | ||
| 69.5 - 74.5 | ||
| 74.5 - 79.5 | ||
| 79.5 - 84.5 | ||
| 84.5 - 89.5 | ||
| 89.5 - 94.5 | ||
| 94.5 - 99.5 |
(b) Draw a histogram to represent the distribution.
(c) Using your histogram, estimate the modal mark.
(d) If a student is chosen at random, find the probability that the student obtains a mark greater than 79.
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Correct Answer: Option n
Explanation:


(a)
(b)
An histogram to represent the distribution of 40 students in an examination.
(c) Modal mark : \(\frac{74.5 + 79.5}{2} = \frac{154}{2} = 77\)
(d) Number of students who obtained marks greater than 79 : 8 + 7 + 2 + 1 = 18.
Total number of students = 40
\(\therefore\) P(mark greater than 79) = \(\frac{18}{40} = \frac{9}{20}\)
(a)
| Class Boundaries | Tally | Frequency |
| 59.5 - 64.5 | || | 2 |
| 64.5 - 69.5 | ||| | 3 |
| 69.5 - 74.5 | |||| | | 6 |
| 74.5 - 79.5 | |||| |||| | | 11 |
| 79.5 - 84.5 | |||| ||| | 8 |
| 84.5 - 89.5 | |||| || | 7 |
| 89.5 - 94.5 | || | 2 |
| 94.5 - 99.5 | | | 1 |
(b)
An histogram to represent the distribution of 40 students in an examination.
(c) Modal mark : \(\frac{74.5 + 79.5}{2} = \frac{154}{2} = 77\)
(d) Number of students who obtained marks greater than 79 : 8 + 7 + 2 + 1 = 18.
Total number of students = 40
\(\therefore\) P(mark greater than 79) = \(\frac{18}{40} = \frac{9}{20}\)