Question

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

Answer 1

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