Finding the 3rd Decile of a Dataset

To find the 3rd decile for the given numbers, we need to follow the steps given below:

Step 1: Sort the numbers in ascending order.

The given numbers are: 15, 10, 20, 25, 18, 11, 9, 12

After sorting them in ascending order, we get: 9, 10, 11, 12, 15, 18, 20, 25

Step 2: Find the total number of observations in the dataset.

In this case, there are 8 numbers.

Step 3: Calculate the position of the 3rd decile.

To find the position of the 3rd decile, we use the formula:

Position of the decile = (n + 1) * d/10

Where n is the total number of observations and d is the decile we want to find (in this case, d = 3).

So, the position of the 3rd decile = (8 + 1) * 3/10 = 2.7

Step 4: Round up the position of the 3rd decile.

Since we cannot have a fractional position, we need to round up the position of the 3rd decile to the nearest whole number.

So, the rounded position of the 3rd decile = 3

Step 5: Find the value at the rounded position of the 3rd decile.

The value at the 3rd decile can be found by looking at the number that corresponds to the rounded position of the 3rd decile in the sorted dataset.

In this case, the value at the 3rd decile is the 3rd number in the sorted dataset, which is 11.

Therefore, the 3rd decile for the given numbers is 11.

Set numbers in Ascending order
9,10,11,12,15,18,20,25

D3=3(n+1/10)
=3(8+1) /10)
=(27/10)
= 2.7
now
2nd term +0.7 (3rd term - 2nd)
10+0.7(11-10)
10+0.7(1)

10.7 will be answer