Q. 55.0( 1 Vote )

# Find the mode for the following data:

Answer :

Observe that, from the given data:

The maximum class frequency, here, is 31 and the class corresponding to this frequency is 80 – 100.

So, this implies that,

Modal class = 80 – 100

Mode of such grouped frequency distribution is given by,

Where,

l = lower limit of the modal class = 80

f_{0} = frequency of the class preceding the modal class = 21

f_{1} = frequency of the modal class = 31

f_{2} = frequency of the class succeeding the modal class = 27

c = size of class interval (the class intervals are same) = 20

∴ Substituting the values l = 80, f_{0} = 21, f_{1} = 31, f_{2} = 27 and c = 20 in the formula of mode. We get

⇒

⇒

⇒

⇒

⇒ Mode = 80 + 14.29

⇒ Mode = 94.29

**Thus, the mode is 94.29**

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