Question

Calculate the media for the following data.

Marks 17 ,20, 22 ,15 ,30 ,25

No. of Students 5 ,9 ,4 ,3 ,10 ,6​

Answer 1

Answer:

• The median of the following data is 22.

Step-by-step explanation:

Given:

• Refer the attach file.

Finding the total number of students:

⟶ n = 5 + 9 + 4 + 3 + 10 + 6

⟶ n = 37

Arranging the marks in ascending order:

Array: 15, 15, 15, 17, 17, 17, 17, 17, 20, 20, 20, 20, 20, 20, 20, 20, 20, 22, 22, 22, 22, 25, 25, 25, 25, 25, 25, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30.

We know that:

If "n" is odd then,

• Median = {(n + 1)/2} th observation

Where,

• n = Total number of students = 37

Finding the median:

⟶ Median = {(37 + 1)/2} th observation

⟶ Median = {(38)/2} th observation

⟶ Median = {19} th observation

⟶ Median = 19th observation = 22

Hence,

• The median of the following data is 22.

Answer 2

Answer:

Given :-

$\begin{gathered}\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7} \tt Marks & \tt 17 & \tt 20 & \tt 22 & \tt 15 & \tt 30 & \tt 25\\\cline{1-7}\tt No\: of\: students & \tt 5 & \tt 9 & \tt 4 & \tt 3 & \tt 10 & \tt 6\\\cline{1-7}\end{tabular}\end{gathered}$

To Find :-

• What is the median.

Formula Used :-

$\clubsuit$ Median Formula if N is odd :

$\longmapsto\sf\boxed{\bold{\pink{Median =\: \bigg\lgroup\bigg(\dfrac{N + 1}{2}\bigg)^{th}\: observations\bigg\rgroup}}}$

where,

• N = Total number of observations.

Solution :-

Given :

$\boxed{\begin{array}{cccc}\sf Marks&\sf No\: of\: students\\\frac{\qquad \qquad \qquad \qquad}{} &\frac{\qquad \qquad \qquad \qquad \qquad}{}\\\sf 17&\sf 5 \\\\\sf 20&\sf 9 \\\\\sf 22&\sf 4 \\\\\sf 15&\sf 3 \\\\\sf 30&\sf 10 \\\\\sf 25&\sf 6\end{array}}$

First, we have to find the total number of students :

$\implies \sf N =\: 5 + 9 + 4 + 3 + 10 + 6$

$\implies \sf N =\: 14 + 4 + 3 + 10 + 6$

$\implies \sf N =\: 18 + 3 + 10 + 6$

$\implies \sf N =\: 21 + 10 + 6$

$\implies \sf N =\: 31 + 6$

$\implies \sf \bold{\purple{N =\: 37}}$

Now, we have to arrange the marks by ascending order :

We have :

• 15 = 3
• 17 = 5
• 20 = 9
• 22 = 4
• 25 = 6
• 30 = 10

So,

$\bigstar$ 15 , 15 ,15 ,17 ,17 ,17 ,17 ,17, 20, 20, 20, 20,20, 20, 20, 20, 22, 22, 22, 22, 22, 25, 25, 25, 25, 25, 25, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30.

Hence, number of observations is odd.

Given :

• Number of observations (N) = 37

So, according to the question by using the formula we get,

$\longrightarrow \sf Median =\: \bigg\lgroup\bigg(\dfrac{37 + 1}{2}\bigg)^{th}\: observations\bigg\rgroup$

$\longrightarrow \sf Median =\: \bigg\lgroup\bigg(\dfrac{\cancel{38}}{\cancel{2}}\bigg)^{th}\: observations\bigg\rgroup$

$\longrightarrow \sf Median =\: \bigg\lgroup\bigg(\dfrac{19}{1}\bigg)^{th}\: observations\bigg\rgroup$

$\longrightarrow \sf Median =\: 19^{th}\: observations$

$\longrightarrow \bold{\red{Median =\: 22}}$

$\therefore$ The median is 22.

[Note : Please refer the attachment. ]