Question

find the median of fallowing numbers.18,19,20,23,22,20,17,19,25 and 21 with step by step explanation​

Answer 1

Step-by-step explanation:

Given :-

Observations are 18,19,20,23,22,20,17,19,25 and 21

To find:-

find the median of the following data

Solution:-

Given observations of the data are

18,19,20,23,22,20,17,19,25 and 21

On writing them into ascending order then

17,18,19,19,20,20,21,22,23,25

Number of observations = 10

we know that

The number of observations of a data is "n" , an even then the median is the average of (n/2)th and (n/2)+1 the observations

we have n=10

n/2 th observation =10/2 = 5

5th observation 20

(n/2)+1 th observation = 5+1 = 6

6th observation = 20

Median =

The average of 5th and 6th observations

=>Median = (20+20)/2

=> Median = 40/2

=> Median = 20

Median = 20

Answer:-

Median of the give data for the given problem is

20

Used formulae:-

The number of observations of a data is "n" , an even then the median is the average of (n/2)th and (n/2)+1 the observations

Additional information:-

• Middle term of the given data when it is arranged in ascending or descending order is called its Median.

• Median is denoted by M

• If the number of observations is n,an even number then the median is the average of (n/2)th and (n/2)+1th observations

• If the number of observations is n ,an odd number then the median is (n+1)/2th observation

Answer 2

Answer:

☘ Given :

Observations - 18,19,20,23,22,20,17,19,25 and 21

☘ Solution :

❍ Arrange the observations in Ascending or Descending Observations

Ascending Order = 17,18,19,19,20,20,21,22,23 and 25

Consider the total no of Observations as n.

$\red {\fbox {n = 10}}$

As , 10 is an even number . So formula of finding median of a even number is :

$\bf {Median} = \frac{1}{2} \frac{ { \frac{n}{2} }^{th}obs + ( \frac{n}{2} + 1 {)}^{th}obs }{} \\ \bf = \frac{1}{2} + ( \frac{10}{2} ^{th} obs \: + ( \frac{10}{2} + 1 {)}^{th} obs) \\ \bf = \frac{1}{2} ( {5}^{th} obs + {6}^{th} obs) \\ \bf \frac{1}{2} + (20 + 20) = \fbox {20}$

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