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The marks obtained by 40 students in an examination are as follows : 85 77 87 74 77 78 ...

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.
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    Correct Answer: Option n
    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) = \(\frac{18}{40} = \frac{9}{20}\)

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