The mode of the following data is $76$ . Calculate the value of $x$ .
Marks $50 - 60$ $60 - 70$ $70 - 80$ $80 - 90$
Students $1$ $2$ $x$ $4$

3

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Solution

The correct option is B $8$

Marks
Students
$50 - 60$
$1$
$60 - 70$
$2 (f_{0})$
$70 - 80$
$x (f_{1})$
$80 - 90$
$4 (f_{2})$

$M o d e = l + (\frac{f_{1} - f_{0}}{{2 f}_{1} - f_{0} - f_{2}}) \times h ⟹ 76 = 70 + (\frac{x - 2}{2 x - 6}) \times 10 ⟹ \frac{6}{10} = \frac{x - 2}{2 x - 6} 6 x - 18 = 5 x - 10 ∴ x = 8$

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Marks	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Students	$12$	$10$	$24$	$5$	$9$

:

Marks	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$
Students	$3$	$4$	$8$	$5$

A biology aptitude test of 50 students was recorded as follows:

$\begin{matrix} M a r k s & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 N o . o f s t u d e n t s & 4 & 8 & 14 & 19 & 5 \end{matrix}$

Draw a histogram from the above data using a graph paper and find the mode value.

A maths aptitude test of 50 students was recorded as follows. Calculate the mode by drawing a histogram.

50

Marks $(%)$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Number of students	$6$	$12$	$14$	$8$	$6$	$4$

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