Answer:
- 2nd decile
- 6th decile
- 8th decile
Step-by-step explanation:
The value of the 2nd decile, 6th decile, and 8th decile are 25.6, 46.6, and 55 respectively.
Further explanation:
A decile divides a set of sorted observations into ten equal parts. Each part represents 1/10 of the sample or population.
First, sort the data in ascending order:
17, 20, 25, 28, 28, 32, 35, 37, 46, 47, 52, 55, 55, 56, 60
The formula for the ith decile is:
=
Solve for the ith decile.
1. 2nd decile: = = 3.2
This means that the value of 2nd decile is between the 3rd and the 4th observations, which are 25 and 28. To determine the exact value of the 2nd decile, we need to interpolate.
a. 28 - 25 = 3 : Get the difference of the 4th and 3rd observations
b. 3.2 - 3 = 0.2 : Ideally, should yield a whole number. If not a whole number, get the decimal difference.
c. (3)*(0.2) = 0.6 : Multiply the results in a. and b.
=> 25 + 0.6 = 25.6 : Add the result in c. to the smaller whole number in a. (3rd observation)
2. 6th decile: = = 9.6
This means that the value of 6th decile is between the 9th and the 10th observations, which are 46 and 47. To determine the exact value of the 6th decile, we need to interpolate.
a. 47 - 46 = 1
b. 9.6 - 9 = 0.6
c. (1)*(0.6) = 0.6
=> 46 + 0.6 = 46.6
3. 8th decile: = = 12.8
This means that the value of 8th decile is between the 12th and the 13th observations, which are 55 and 55. To determine the exact value of the 8th decile, we need to interpolate.
a. 55 - 55 = 0
b. 12.8 - 12 = 0.8
c. (0)*(0.8) = 0
=> 55 + 0 = 55
