What will be the mode of the given data?

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12.44

13.44

14.44

15.44

answer is A.

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Detailed Solution

We have to find the mode of the given data:
Question Image

We know that the empirical formula of mode is,

Mode = 3 median − 2 mean

The total number of students is 25.
Multiplying the marks by the number of students.
Question Image

We know that,

mean = sum of all observations number of observations

mean = 30 + 55 + 48 + 65 + 28 + 48 + 38 + 20 25 = 13.28

So, the mean of the data is 13.28.
Calculating the median,
Rearranging the data in ascending order:
10,10,10,11,11,11,11,11,12,12,12,12,13,13,13,13,13,14,14,16,16,16,19,19,20
The number of observations is 25, which is odd.

n + 1 2 t h term = 25 + 1 2 t h term = 262 t h term = 13 t h term = 13

So, the median of the data is 13.
Calculating the mode,
Putting 13.28 for mean and 13 for the median in:

Mode = 3 median − 2 mean

Mode = 3 × 13 − 2 × 13.28 = 39 − 26.56 = 12.44

So, the mode of the given data is 12.44.
Therefore, option 1 is correct.

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