Question

Find the mode of the following distribution :
Classes : 0 - 20 20 – 40 40 – 60 60 – 80 80 – 100
Frequency: 10 8 12 16 |​

Answer 1

Step-by-step explanation:

I hope my answer are right

Answer 2

The mode of the given data is 65.

Correct Question: Find the mode of the following distribution :

Classes : 0 - 20 20 – 40 40 – 60 60 – 80 80 – 100

Frequency: 10 8 12 16 4

Given:

Classes : 0 - 20 20 – 40 40 – 60 60 – 80 80 – 100

Frequency: 10 8 12 16 4

To Find:

The mode of the given data.

Solution:

The mode of any given data is found using the formula

${\rm Mode}=l+h(\frac{f_m-f_1}{2f_m-f_1-f_2})$, where 'l' is the lower boundary of the modal class, 'h' is the size of the modal class, $f_m$ is the frequency corresponding to the modal class, $f_1$ is the frequency preceding to the modal class, and $f_2$ is the frequency proceeding to the modal class.

In the given data, the class having maximum frequency is 60 – 80. So, $l=60$,  $h=20$, $f_m=16$, $f_1=12$, and $f_2=4$.

Substitute these values into the formula of mode.

${\rm Mode}=60+20(\frac{16-12}{2\cdot 16 -12-4})\\=60+20(\frac{4}{32-16})\\ =60+20(\frac{4}{16})\\=60+5\\=65$

Thus, the mode of the given data is 65.