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The mode (correct to two decimal places) for the given data is:

 Class-   interval

Frequency

 0-10

 6 

 10-20

 9

 20-30

 8

 30-40

 14

 40-50

 28

 50-60

 20

 60-70

 11

 70-80

 9


1. 39.34
2. 46.36
3. 28
4. 52.54

1 Answer

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Best answer
Correct Answer - Option 2 : 46.36

Formula used

\(\rm Mode =L + \left [ \frac{f1 - f0}{2f1 - f0 - f2} \right ]\times i\)

i = class interval or class size

f1 = frequency of modal class

fo = frequency of pre modal class

f2 = frequency of success modal class

L = lower limit of modal class

Calculation:

Here maximum frequency is 28 ,the class corresponding to this 40-50

So modal class is 40-50

Now lower limit of modal class (l) = 40

Frequency (f1) of modal class = 28

frequency (f0) of preceding the modal class  = 14

frequency (f2) of the class succeeding the modal class = 20

Class size = 10    

\(\rm Mode = 40 + \left [ \frac{28 - 14}{2 \times 28 - 14 - 20} \right ]\times 10\)

= 40 + 6.36

∴ Mode = 46.36

Another formula to calculate mode = 3 Median - 2 Mean 

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