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Question

Calculate mode from following data:

Class Interval51415242534354444545564Frequency81015254020.

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Solution

Lets form the frequency table by converting into continuous class interval for finding mode.

Class Intervalxf5144.514.58152414.524.510253424.534.515354434.544.525 [f0]4554 [L] 44.554.540 [f1]556454.564.520 [f2]
In frequency, 40 is the highest frequency.

Modal class =44.554.5

From the table,

L=44.5 [Lower boundary]

f1=40

f0=25

f2=20

Size of the class interval (h)=10

Mode =L+(f1f02f1(f0+f2))h

=44.5+(40252(40)(25+20))10

=44.5+(158045))10

=44.5+15035

=44.5+4.28 (Approximately)

=48.78 (Approximately)

Thus, the mode of the given data is 48.78.


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