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.
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.
Explanation
(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) = \(\frac{18}{40} = \frac{9}{20}\)
