Question

Find the median and mode of the following data:11,13,17,11 18,1921,23,11,12,10​

Answer 1

Median :-

Ascending order :- 10 ,11,11,11, 12 ,13 , 17 , 18 , 19 , 21 , 23

13 is the median .

Mode :-

11 is the mode because it repeated more .

Answer 2

$\huge\texttt{Question:}$

Find the median and mean of the following data :

11 , 13 , 17 , 11 , 18 , 19 , 21 , 23 , 11 , 12 , 10

$\huge\texttt{Answer:}$

First , of all we need to know , what a certain set of observations is . The observations given above , are called information . This is because they are mot ordered in any sequence , either ascending or descending . Whenever , this set of information is ordered in either ascending or descending order , then it is called $\textbf{data}$ .

Now next up , you need to know what mode and median are . So following are the definitions of mean and median :-

$\textbf{Mode:}$ Mode is simply , the highest occurring observation in a whole set of data .

For example :- 1 , 5 , 3 , 5 , 2 , 5 .

In this set of information , the highest occurring observation is 5 . So , the mode of the information would be 5 .

N.B - Mode can be found without arranging the observations as well , but arranging the set of information really helps in improving accuracy of our result .

$\textbf{Median:}$ Median is simply the middle observation of a set of arranged information either in ascending or in descending order . Median can be found in two ways :-

If number of observations , n is odd , then median = $\frac{n + 1}{2}th$ observation .

For example :- 11 , 21 , 13 , 12 , 15 , 16 , 17 , 19 , 18 .

The arranged form would be :

11 , 12 , 13 , 15 , 16 , 17 , 18 , 19 , 21

Here , Number of observations = 9

Therefore , Median = $\frac{9+1}{2}th$ observation .

= 5 th observation .

The median ultimately = 16 .

If number of observations n , is even ,

then median =

$({\frac{n}{2}th \: observation + \frac{n}{2} + 1}th\:observation )\times \frac{1}{2}$

For example :- 25 , 34 , 31 , 23 , 22 , 26 , 35 , 28 , 20 , 32

The arranged form would be :

20 , 22 , 23 , 25 , 26 , 28 , 31 , 32 , 34 , 35

Here , number of observations = 10

Therefore , $\frac{n}{2}th observation = 5\:th\:observation = 26$

And , $\frac{n}{2}+1\:th\:observation = 6\:th\:observation = 28$

Therefore , median = $\frac{26 + 28}{2} = 27$

So , now that all the related topics are clear , we can move towards the question .

The arranged form would be :

10 , 11 , 11 , 11 , 12 , 13 , 17 , 18 , 19 , 21 , 23

Number of observations = 11

Therefore , Median =

$\frac{11 + 1}{2}th\:observation = 6th\:observation = 13$

Since , highest occurring observation is 11 , ( it occurred 3 times )

Therefore , Mode = 11