Question

Find the median of the first four even numbers.​

Answer 1

Given,

The first four even numbers.

To find,

The median of the given numbers.

Solution,

We know that an even number is a number that is divisible by 2.

The first four even numbers are 2, 4, 6, and 8.

To find the median, we have to sum the numbers and then divide them by the count of the numbers present.

Median = (2+4+6+8)/4

⇒ Median = 5

Hence, the median of the first four even numbers is 5.

Answer 2

Median of of the first four even numbers is 5

Given :

The first four even numbers.

To find :

Median of first four even numbers.

Concept :

Median :

Median is the middle most value of a set of observations when the samples are arranged in order of magnitudes ( Either in ascending or in descending)

Formula for calculating median :

1. If total number of observations n is odd then

$\displaystyle \sf{ Median = {\bigg( \frac{n + 1}{2} \bigg)}^{th} \: observation }$

2. If total number of observations n is even then

$\displaystyle \sf{ Median = \frac{1}{2} \times \bigg[ {\bigg( \frac{n }{2} \bigg)}^{th} \: observation +{\bigg( \frac{n}{2} + 1 \bigg)}^{th} \: observation \bigg] }$

Solution :

Step 1 of 3 :

Write down the given numbers

Here the first four even numbers are 2 , 4 , 6 , 8

Step 2 of 3 :

Rearrange in ascending order

The numbers 2 , 4 , 6 , 8 are already in ascending order

Step 3 of 3 :

Find the median of the numbers

Number of observations = 4 which is even

Therefore the required median

= The middle terms of the whole arranged observations

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {\bigg( \frac{n }{2} \bigg)}^{th} \: observation +{\bigg( \frac{n}{2} +1 \bigg)}^{th} \: observation \bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {\bigg( \frac{4 }{2} \bigg)}^{th} \: observation +{\bigg( \frac{4}{2} + 1 \bigg)}^{th} \: observation \bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ {2}^{nd} \: observation +{3}^{rd} \: observation \bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times (4 + 6) }$

$\displaystyle \sf{ = \frac{1}{2} \times 10 }$

$\displaystyle \sf{ = 5 }$

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