Question

find the median of 54,63,66,72,98,87,92?​

Answer 1

Answer:

72

Step-by-step explanation:

Median is the middlemost value in the given observations

To find the median of some given numbers, first we should arrange them in ascending order

Ascending order of 54,63,66,72,98,87,92 is

54 , 63 , 66 , 72 , 87 , 92 , 98

Now we should count the number of elements

There are 7 numbers totally (7 is odd number)

The formula for finding the median of given numbers ( when the total number of elements is an odd number -> 7 is odd ) is :

[ ( n + 1 ) / (  2 ) ] th term

Where n is the number of elements

Applying n = 7 in the given formula :

The median = [ ( 7 + 1 ) / (  2 ) ] th term

= [ ( 8 ) / (  2 ) ] th term

= 4 th term

The 4 th term in the series (ascending order) is 72

Hence the median of the given observations is 72

Answer 2

★ How to do :-

Here, we are given with seven observations in which we are asked to find the median of those values. We know that the median is the middle value of any data, but the condition is that the data should be arranged in ascending or descending order. I'll arrange in ascending order. We have two methods to solve this problem i.e, to find the median of the data. We will solve both methods here. One is we solve the problem by using a specific formula. The other is we find logically. So, let's solve!!

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➤ Solution :-

Ascending order :-

${\tt \leadsto 54, 63, 66, 72, 87, 92, 98}$

Method 1 :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{n + 1}{2} \: \: th \: \: term}}}$

Substitute the value of n.

${\tt \leadsto \dfrac{7 + 1}{2} \: \: th \: \: term}$

Add the numbers in the numerator, first.

${\tt \leadsto \dfrac{8}{2} \: \: th \: \: term}$

Simplify the fraction obtained.

${\tt \leadsto \cancel \dfrac{8}{2} = 4th \: \: term}$

We can see that the 4th term in ascending order is 72. So,

${\sf \leadsto \pink{\underline{\boxed{\sf Median = 72}}}}$

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Method 2 :-

${\tt \leadsto 54, 63, 66, 72, 87, 92, 98}$

Cancel each number equal number of times from LHS and RHS.

${\tt \leadsto \cancel{54} , \cancel{63} , \cancel{66} , 72, \cancel{87} , \cancel{92} , \cancel{98}}$

We can see that the remaining number is 72. So,

${\sf \leadsto \pink{\underline{\boxed{\sf Median = 72}}}}$

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$\dashrightarrow$ Formulas of median:-

${\sf \to {Median}_{(Even \: observations)} = \dfrac{n}{2} + 1th \: \: term}$

${\sf \to {Median}_{(Odd \: observations)} = \dfrac{n + 1}{2} th \: \: term}$