Calculate the Mode of the Following Distribution: - Mathematics

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Sum

Calculate the mode of the following distribution:

Class 10 − 15 15 − 20 20 − 25 25 − 30 30 − 35
Frequency 4 7 20 8 1
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Solution

Modal class is the class with the highest frequency
modal class is 20 - 25
lower limit of modal class i.e l = 20
class size i.e h = 5
frequency of modal class f1 = 20
frequency of preceding class f0 = 7
frequency of succeeding class f2 = 8
Using the formula
mode = `l + (( f_1 − f_0)/(2f_1 − f_0 − f_2)) xx h`

Plugging the values in the formula we get
mode = `20 + ( 20 −7)/( 2 × 20 − 7 − 8) xx 5`

mode = `20 + (13)/(25) xx 5`

mode = `20+13/5`

mode = `113/5` = 22.6

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2018-2019 (March) 30/4/3

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Activity:

From the given table,

Modal class = `square`

∴ Mode = `square + [(f_1-f_0)/(2f_1-f_0 - square)]xxh`

∴ Mode = `3.5 + [(40-33)/(2(40)-33-27)]xxsquare`

∴ Mode = `3.5 +[7/(80-60)]xx3`

∴ Mode = `square`

∴ The mode of the volume of petrol filled is `square`.


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