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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
Concept: Mode of Grouped Data
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