Question

the
10. Find the mode of
distribution table
fuequency
C. I
0-10
10-20 20-30 30 40
f
2
3
5
2​

Answer 1

Question:-

Find the mode of the following data:-

$\boxed{\begin{array}{c|c} \bf{Class} & \bf{Frequency} \\ \dfrac{\qquad\qquad}{} & \dfrac{\qquad\qquad}{} \\ \sf{0-10} & \sf{2} \\ \sf{10-20} & \sf{3} \\ \sf{20-30} & \sf{5} \\ \sf{30-40} & \sf{2}\end{array}}$

Solution:-

Let us find the modal class of the given data.

We know:-

$\sf{\red{\underline{Modal\:class:-}}}$

• The class with highest frequency is known as the modal class.

Here,

Class 20-30 has the highest frequency of 5. Hence, it is the modal class of the given data.

Now,

We know,

• $\dag{\boxed{\underline{\blue{\rm{Mode = l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h}}}}}$

Where:-

• l = lower limit of the modal class
• h = height of the class
• f₀ = frequency of the preceding class
• f₁ = frequency of the modal class
• f₂ = frequency of the succeeding class.

Here:-

• l = 20
• h = 30 - 20 = 10
• f₀ = 3
• f₁ = 5
• f₂ = 2

Putting all the values in the formula:-

$\sf{Mode = 20 + \dfrac{5 - 3}{2 \times 5 - 3 - 2} \times 10}$

$= \sf{Mode = 20 + \dfrac{2}{10 - 5} \times10 }$

$= \sf{Mode = 20 + \dfrac{2}{5} \times 10}$

$= \sf{Mode = 20 + \dfrac{2}{\not{5}} \times \not{10}}$

$= \sf{Mode = 20 + 2 + 2}$

$= \sf{Mode = 24}$

$\underline{\overline{\boxed{\green{\sf{\therefore\:The\:mode\:of\:the\:following\:data\:is\:24}}}}}$

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