Find the mode of the following data.
Number
$0 - 3$
$3 - 6$
$6 - 9$
$9 - 12$
$12 -$
$15 - 18$
$18 - 19$
$21 -$
Frequency
$4$

$9$
$7$
$6$
$3$
$1$

19

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31

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26

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21

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Solution

The correct option is C $26$
The maximum frequency is $18,$ the class corresponding to that frequency is equal to $3 - 6$
We have to apply the formula Mode $= L + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$
Where L is the lower class limit of the modal class $= 3$
$f_{1}$ is the frequency of the modal class $= 18$
$f_{0}$ is the frequency of the class before the modal class in the frequency table $= 4$
$f_{2}$ is the frequency of the class after the modal class in the frequency table $= 9$
h is the class interval of the modal class $= 3$
Mode $= 3 + [(18 - 4) / ([2 \times 18] - 4 - 9)] \times 3$
$= 3 + [(14) / 36 - 4 - 9] \times 3$
$= 3 + [23 / 3] \times 3$
$= 3 + 23$
Hence, Mode $= 26$

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Similar questions

Class:	$3 - 6$	$6 - 9$	$9 - 12$	$12 - 15$	$15 - 18$	$18 - 21$	$21 - 24$
Frequency:	$2$	$5$	$10$	$23$	$21$	$12$	$3$

Prepare a frequency distribution by inclusive method taking class interval of 7 from the following data:

Number	$12$	$13$	$14$	$15$	$16$	$17$
Frequency	$7$	$9$	$6$	$22$	$20$	$19$

$x$	$15$	$16$	$17$	$18$	$19$	$20$	$21$	$22$	$23$
$f$	$6$	$7$	$9$	$13$	$10$	$12$	$8$	$0$	$4$

:

Number	$0$	$3$	$6$	$9$	$12$	$15$	$18$
Frequency	$4$	$8$	$9$	$7$	$10$	$3$	$10$

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Number	$0 - 3$	$3 - 6$	$6 - 9$	$9 - 12$	$12 -$	$15 - 18$	$18 - 19$	$21 -$
Frequency	$4$		$9$	$7$	$6$	$3$	$1$