Question

Find the mode for the following distribution table.
Class Interval. | frequency
20-30. | 4
30-40. | 7
40-50. | 9
50-60. | 11
60-70. | 6
70-80. | 2​

Answer 1

Answer:

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Answer 2

Frequency distribution table

$\begin{lgathered}\boxed{\begin{array}{c|c} \bf{Class} & \bf{Frequency} \\ \dfrac{\qquad\qquad}{} & \dfrac{\qquad\qquad}{} \\ \sf{20 - 30} & \sf{4} \\ \sf{30 - 40} & \sf{7} \\ \sf{40 - 50} & \sf{9} \\ \sf{50 - 60} & \sf{11} \\ \sf{60 - 70} & \sf{6} \\ \sf{70 - 80} & \sf{2}\end{array}}\end{lgathered}$

⠀

Modal Class: Class having the greatest frequency is called modal class.

Here,

• Modal class = 50 - 60

Then,

• $\sf{f_0 = 9}$
• $\sf{f_1 = 11}$
• $\sf{f_2 = 6}$
• $\sf{l = 50}$
• $\sf{i = 10}$

⠀

Formula used

$\large{\bf{\longmapsto{\boxed{\pink{Z = l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times i}}}}}$

⠀

Putting all the values

$\tt\dashrightarrow{Mode = 50 + \dfrac{11 - 9}{2(11) - 9 - 6} \times 10}$

⠀

$\tt\dashrightarrow{Mode = 50 + \dfrac{2}{22 - 15} \times 10}$

⠀

$\tt\dashrightarrow{Mode = 50 + \dfrac{2}{7} \times 10}$

⠀

$\tt\dashrightarrow{Mode = 50 + \dfrac{20}{7}}$

⠀

$\tt\dashrightarrow{Mode = 50 + 2.85}$

⠀

$\bf\dashrightarrow{\purple{Mode = 52.85}}$

⠀

⠀⠀$\underline{\sf{Thus,\: mode\: of\: the\: data\: is\: 52.85.}}$