Question

Find the mode of the following frequency distribution.
Class: 0-10, 10-20, 20-30, 30-40, 40-50.
Frequency: 8, 12, 10, 11, 9.
(A)18.6
(B)16.6
(C)20.5​

Answer 1

S O L U T I O N :

We have data give;

CLASS - INTERVAL : 0 - 10, 10 - 20, 20 - 30, 30 - 40, 40 - 50

FREQUENCY : 8, 12, 10, 11, 9

$\underline{\bf{Explanation\::}}$

As we know that formula of the mode;

$\boxed{\bf{Mode= l+\bigg(\frac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h}}$

Where as;

• l is the lower limit of class - interval = 10
• f1 is the frequency of class - interval = 12
• f0 is the frequency of previous of class - interval = 8
• f2 is the frequency of next of class - interval = 10
• h is the size of class - interval = 10

∴ Putting the values of the given formulas :

$\mapsto\tt{Mode = l+\bigg(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg)\times h}$

$\mapsto\tt{Mode = 10+\bigg(\dfrac{12 - 8}{2(12) - 8 - 10} \bigg)\times 10}$

$\mapsto\tt{Mode = 10+\bigg(\dfrac{4}{24 - 18} \bigg)\times 10}$

$\mapsto\tt{Mode = 10+\dfrac{4}{6} \times 10}$

$\mapsto\tt{Mode = 10+\cancel{\dfrac{40}{6} }}$

$\mapsto\tt{Mode = 10+6.66}$

$\mapsto\bf{Mode =16.6}$

Thus;

The value of the mode will be 16.6 .

Option (B)

Answer 2

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