2. The median of 19 observations is 30. Two more observations aremade

1.	2. The median of 19 observations is 30. Two more observations aremade and the values of these are 8 and 32. Find the median of the 21observations taken together.
Answer» Answer : Median = 30 Step-by-step explanation : $\underline{\underline{\bf Median:}}$ ⇒ Median is the middle number when the given data is ARRANGED in either ASCENDING or DESCENDING order. ⇒ If there are 2 numbers in the middle, the median is the average of those 2 numbers. ⇒ The median value is fixed by its position and is not reflected by the individual value. ⇒ Median is not dependent on all the data values in a dataset. ⇒ n = number of observations If n = odd, $\boxed{\bf Median=(\frac{n+1}{2})^{th} \ term}$ If n = even, $\boxed{\bf Median =\frac{[(\frac{n}{2})^{th} +(\frac{n}{2} +1)^{th}]}{2} term}$ ____________________________________ Given, The median of 19 observations is 30. Two more observations are MADE and the values of these are 8 and 32. new observations are 8 and 32. => 8 is less than 30 => 32 is more than 30 So, the middle value does not change as the two observations are added on either side of 30. ∴ Median of 21 observations = 30

2. The median of 19 observations is 30. Two more observations aremade and the values of these are 8 and 32. Find the median of the 21observations taken together.

Answer»

Median = 30

$\underline{\underline{\bf Median:}}$

⇒ Median is the middle number when the given data is ARRANGED in either ASCENDING or DESCENDING order.

⇒ If there are 2 numbers in the middle, the median is the average of those 2 numbers.

⇒ The median value is fixed by its position and is not reflected by the individual value.

⇒ Median is not dependent on all the data values in a dataset.

⇒ n = number of observations

If n = odd,

$\boxed{\bf Median=(\frac{n+1}{2})^{th} \ term}$

If n = even,

$\boxed{\bf Median =\frac{[(\frac{n}{2})^{th} +(\frac{n}{2} +1)^{th}]}{2} term}$

____________________________________

Given,

new observations are 8 and 32.

=> 8 is less than 30

=> 32 is more than 30

So, the middle value does not change as the two observations are added on either side of 30.

∴ Median of 21 observations = 30