Discussion

Find the mode for the following data:

Class Interval	0-10	10-20	20-30	30-40	40-50
Frequency	5	8	15	12	7

Answer: C

Correct answer: 27.00

The modal class is the one with the greatest frequency: 20–30, with a frequency of 15.

\[\text{Mode} = L + \frac{f_m - f_1}{2f_m - f_1 - f_2} \times h\]

Here \(L = 20\), \(h = 10\), \(f_m = 15\), the preceding frequency \(f_1 = 8\) and the succeeding frequency \(f_2 = 12\).

\[\text{Mode} = 20 + \frac{15 - 8}{2(15) - 8 - 12} \times 10 = 20 + \frac{7}{10} \times 10 = 27\]

The mode sits above the midpoint of its class because the class after it is heavier than the class before it.

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