For the following marks distribution of 5 students in an examination, match column-I with the datas given in column-II.
Class interval 0-10 10-20 20-30 30-40
No. of students 1 3 0 1
Here,
$x_{k} =$ lower limit of the modal class interval $h =$ width of the class interval
$f_{k} =$ frequency of the modal class $f_{k - 1} =$ frequency of the class proceeding the modal class
$f k + 1 =$ frequency of the class succeeding the modal class
Find $A, B, C, D$

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Solution

In the given distribution table, the frequency $3$ is highest for the class $10 - 20$
Hence, modal class $= 10 - 20$
Now, lower limit of the modal class interval $x_{k} = 10$

Frequency of the modal class $= f_{k} = 3$
Frequency of the class preceeding the modal class $f_{k - 1} = 1$
And, width of the class interval $h = 10$
Hence, $A - 2, B - 1, C - 5, D - 2$

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Similar questions

In the formula for finding mode of a grouped data,

Mode = $X + (\frac{A - B}{2 A - B - C}) \times h$

$\begin{matrix} i) X & a) f r e q u e n c y o f t h e c l a s s p r e c e d i n g t h e m o d a l c l a s s i i) A & b) L o w e r l i m i t o f t h e m o d a l c l a s s i i i) B & c) frequency of the class succeeding the modal class i v) C & d) f r e q u e n c y o f t h e m o d a l c l a s s \end{matrix}$

Match the options.

The modal value will be closer to the lower limit of the modal class if the preceding class has a higher frequency than the succeeding class.

Q. The modal class of the frequency distribution given below is

Class	0-10	10-20	20-30	30-40	40-50
Frequency	7	15	13	17	10

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