The following data gives marks obtained by students in an exam.

$\begin{matrix} M a r k s & N o . o f s t u d e n t s A b o v e 0 & 80 A b o v e 10 & 77 A b o v e 20 & 72 A b o v e 30 & 65 A b o v e 40 & 55 A b o v e 50 & 43 A b o v e 60 & 23 A b o v e 70 & 16 A b o v e 80 & 10 A b o v e 90 & 8 A b o v e 100 & 0 \end{matrix}$

(i) Convert to a regular distribution.

(ii) Find the mode. [3 MARKS]

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Solution

Table: 1 Mark
Formula: 1 Mark
Application: 1 Mark

$\begin{matrix} M a r k s & N o . o f s t u d e n t s A b o v e 0 & 80 A b o v e 10 & 77 A b o v e 20 & 72 A b o v e 30 & 65 A b o v e 40 & 55 A b o v e 50 & 43 A b o v e 60 & 23 A b o v e 70 & 16 A b o v e 80 & 10 A b o v e 90 & 8 A b o v e 100 & 0 \end{matrix}$

Converting to regular frequency distribution,

$\begin{matrix} C l a s s I n t e r v a l & S t u d e n t 0 - 10 & 3 10 - 20 & 5 20 - 30 & 7 30 - 40 & 10 40 - 50 & 12 50 - 60 & 20 60 - 70 & 7 70 - 80 & 6 80 - 90 & 2 90 - 100 & 8 \end{matrix}$

Modal Class is 50-60

Mode
$= I + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$

$= 50 + \frac{20 - 12}{40 - 12 - 7} \times 10$

$= 53.81$

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Similar questions

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The following data gives marks obtained by students in an exam. MarksNo. of studentsAbove 080Above 1077Above 2072Above 3065Above 4055Above 5043Above 6023Above 7016Above 8010Above 908Above 1000 (i) Convert to a regular distribution. (ii) Find the mode. [3 MARKS]