Question

Find the mode of the following data.
Class internal Frequency
0 - 10
10 - 20
20-30
30-40
40 - 50
6.
9
15
9
1
N= 40​

Answer 1

Answer:

The mode of the given data is 25.

Step-by-step explanation:

$\begin{tabular}{|c|c|}\cline{1-2} Class Interval & Frequency \\\cline{1-2}\ 0-10 & 6 \\\cline{1-2}\ 10-20 & 9 \\\cline{1-2}\ 20-30 & 15 \\\cline{1-2}\ 30-40 & 9 \\\cline{1-2}\ 40-50 & 1 \\\cline{1-2}\end{tabular}$

(In case you're an app user, kindly refer the attachment for the better understanding of class intervals and its frequency)

The mode is the data value that appears most often in the given set of data.

Maximum frequency is from class 20-30. So, it's the modal class.

Class size = 10

Lower limit of modal class = 20

Frequency of modal class = 15

Frequency (class preceding the modal class) = 9

Frequency (class after the modal class) = 9

• h = 10
• I = 20
• f₁ = 15
• f₀ = 9
• f₂ = 9

$\boxed{\sf{Mode = l + \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h}}$

$\sf{\longrightarrow} \: Mode = 20+ \left[ \dfrac{15 - 9}{2(15) - 9 - 9} \right] \times 10$

$\sf{\longrightarrow} \: Mode = 20+ \left[ \dfrac{6}{30 - 18} \right] \times 10$

$\sf{\longrightarrow} \: Mode = 20+ \dfrac{6}{12} \times 10$

$\sf{\longrightarrow} \: Mode = 20+ \dfrac{1}{2} \times 10$

$\sf{\longrightarrow} \: Mode = 20+5$

$\sf{\longrightarrow} \: Mode = 25$

Mode = 25

Therefore, the mode of the given data is 25.

Answer 2

Answer:

• Mode (z) = 25

Step-by-step explanation:

What is mode?

• The term that occurs most of the time in the given table is known as mode.
• It is denoted by alphabet z.

$\begin{tabular}{|c|c|} \cline{1-2} Class & Internal\;Frequency\;(f) \\ \cline{1-2} 0-10 & 6 \\ \cline{1-2}10-20 & 9 \\ \cline{1-2} 20-30 & 15 \\\cline{1-2} 30-40 & 9 \\\cline{1-2} 40-50 & 1 \\\cline{1-2} & N=40 \\\cline{1-2}\end{tabular}$

Here,

• Model class = 20 - 30 (Maximum Frequency)
• Size of class interval (c) = 10
• Frequency of model class (F₁) = 15
• Frequency of preceding class (F₀) = 9
• Frequency of succeeding class (F₂) = 9
• Lower limit (L) = 20

Now, we know the formula

$\implies{\tt{Mode\;(z)=L + \dfrac{F_{1}-F_{0}}{2F_{1}-F_{0}-F_{2}}\times c}}$

Put the values in the formula,

$\implies{\tt{Mode\;(z)=20 + \dfrac{15-9}{2(15)-9-9}\times 10}}$

$\implies{\tt{Mode\;(z)=20 + \dfrac{6}{30-18}\times 10}}$

$\implies{\tt{Mode\;(z)=20 + \dfrac{6}{12}\times 10}}$

$\implies{\tt{Mode\;(z)=20 + \dfrac{60}{12}}}$

$\implies{\tt{Mode\;(z)=20 + 5}}$

$\implies{\boxed{\tt{Mode\;(z)=25}}}$