Answer:
25th percentile = 15
75th percentile = 22
Step-by-step explanation:
To find the percentile values in a data set, the first step is to arrange the date in ascending order
The given data is already in ascending order and there are 10 data points
Let's examine some terms relating to percentile:
First Quartile(25th percentile)
- The first quartile (Q1) is the data value that separates the bottom 25% and top 75% of the data which is arranged in ascending order. So, the first quartile has 25% of the items lower than it and 75% of items greater than it. This is equal to the 25th percentile of the data set.
Third Quartile(75th percentile)
- The third quartile (Q3) is the data value that separates the bottom 75% and top 25% of the data which is arranged in ascending order. So, the third quartile has 75% of the items lower than it and 25% of items greater than it. This is equal to the 75th percentile of the data set.
Here are the steps to compute the quartile(percentile values):
- Arrange the data in ascending order (done)
- Find the median of the data values. This is the second quartile(Q2)
Since there are 10 data points, the median is the average of the 5th and 6th data points = (20 + 22)/2 = 21
- Find the median of the data values which are below the second quartile. This is the first quartile.
There are 5 values below 21:
12, 12, 15, 17, 20
The median is the middle value which is 15
- Find the median of the data values which are above the second quartile. This is the third quartile.
There are 5 values above 21:
22, 22, 22, 28, 30
- The median is the middle of these which is 22
- Hence
First Quartile = 25 percentile = 15
Second Quartile = 75 percentile = 22
