Question

calculate the mean and median of the data given blow 80,35,40,41,25 43,48,52,54,75,35​

Answer 1

For mode we get the sum is 528 and by dividing it by 11 we get 48 which is the mean(average)

Median is 43 as it is the observations are odd 43 is in middle so it is the median

Answer 2

Given :

80,35,40,41,25,43,48,52,54,75,35.

To Find :

The mean and median.

Solution :

Mean :

We can see that here we have a total of 11 observations.

So,

Mean = Sum of observations/Total no of observations

where,

• The observations = 80,35,40,41,25,43,48,52,54,75,35.
• Total no of observations = 11

Substituting the values,

⇒ Mean = (80 + 35 + 40 + 41 + 25 + 43 + 48 + 52 + 54 + 75 + 35)/11

⇒ Mean = 4587/11

⇒ Mean = 417

$\qquad\quad\therefore\boxed{\bf{\pink{Mean=417.}}}\green{\bigstar}$

Median :

First we have to arrange the observations in ascending order.

So,

In ascending order : 25, 35, 35, 40, 41, 43, 48, 52, 54, 75, 80.

Here we can see that the total no of observations (n) = 11, which is odd.

☯ According to the question,

$\bf Median=\left(\dfrac{n+1}{2}\right)th\ term$

where,

• n = 11

Substituting the values,

$\\ \Rightarrow\sf Median=\left(\dfrac{11+1}{2}\right)th\ term$

$\\ \Rightarrow\sf Median=\left(\dfrac{12}{2}\right)th\ term$

$\\ \Rightarrow\sf Median=\left(\dfrac{\cancel{12}\ \ ^6}{\not{2}}\right)th\ term$

$\\ \Rightarrow\sf Median=6th\ term$

From the observations we can see that,

$\\ \Rightarrow\sf Median=43$

$\qquad\quad\therefore\boxed{\bf{\pink{Median=43.}}}\green{\bigstar}$

Explore More :

• When n is even then median,

$\bf Median=\left[\dfrac{\left(\dfrac{n}{2}\right)th\ term+\left(\dfrac{n+1}{2}\right)th\ term}{2}\right]$

where,

• n = no of observations