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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 f_{1 }= 20
frequency of preceding class f_{0 }= 7
frequency of succeeding class f_{2 }= 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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Activity:
From the given table,
Modal class = `square`
∴ Mode = `square + [(f_1f_0)/(2f_1f_0  square)]xxh`
∴ Mode = `3.5 + [(4033)/(2(40)3327)]xxsquare`
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∴ Mode = `square`
∴ The mode of the volume of petrol filled is `square`.