The scores (out of 100) obtained by 33 students in a mathematics test are as follows.
69, 48, 84, 58, 48, 73, 83, 48, 66, 58, 84, 66, 64, 71, 64, 66, 69, 66, 83, 66, 69, 71, 81, 71, 73, 69, 66, 66, 64, 58, 64, 69, 69.
Represent this data in the form of a frequency distribution.

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Solution

The number of students who have the same marks in mathematics is the frequency of that mark.
A frequency distribution table for the given data is given below.

$\begin{matrix} Scores & Tally marks & Frequency 48 & | | | & 3 58 & | | | & 3 64 & | | | | & 4 66 & / | | | | | | & 7 69 & / | | | | | & 6 71 & | | | & 3 73 & | | & 2 81 & | & 1 83 & | | & 2 84 & | | & 2 Total & 33 \end{matrix}$

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100

33

69, 48, 84, 58, 48, 73, 83, 48, 66, 58, 84 66, 64, 71, 64, 66, 69, 66, 83, 66, 69, 71 81, 71, 73, 69, 66, 66, 64, 58, 64, 69, 69

tan 69^{\circ} + tan 66^{\circ} - tan 69^{\circ} tan 66^{\circ} = 2 k, t h e n 2 k =

tan 69^{o} + tan 66^{o} - tan 69^{o} tan 66^{o} = 2 k

k = ?

\frac{\tan 69 ° + \tan 66 °}{1 - \tan 69 ° \tan 66 °} = - 1

\frac{tan 69^{o} + tan 66^{o}}{1 - tan 69^{o} tan 66^{o}} = - 1

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