Q1 is the value that represents the top of the first 25% of the data.
Q2 or the median is a value that represents the 50% point in the data and is the center number
Q3 represents the value with 75% of the data below it
Q4 is the max value in the data
NOTE: The stretch between Q1 and Q3 is called the IQR (inter quartile range). This represents 50% of the dataset in its middle.
Example- follow the steps:
Step 1: Put the data in order.
Dataset (placed in order) – the data must be in order first
1, 3, 5, 7, 9, 11,13, 15, 17, 19
To get Q1 you need 25% of the data to the left and 75% to the right
Step 2: Multiply the number of values you have – there are 10 values here – times the quartile you want (Q1 = .25)
.25 * 10 = 2.5
Then, look at the result. In this case the result is 2.5 (a decimal value).
When the value is not a whole number, such as 2.5 in this case, you round it UP to the next whole number, which is 3 in this case.
Step 3: This tells you that the Q1 is the third number in the dataset (assuming the dataset is in order)
1, 3, Q1 = 5, 7, 9, 11, 13, 15, 17, 19
Therefore, below the value 5 (the third number in the dataset) are 25% of the values and above the value 5 are 75% of the dataset values.
NEXT Finding Q2 (the median)
Step 1: Multiple .5 ( because Q2 is 50% ) times the number of values in your dataset. This is the same process you can use for any quartile or percentile.
.5*10 = 5
This is a WHOLE number (not a decimal). So, the median is the average of that fifth and sixth dataset values. This takes some getting used to so let’s review. If the value is whole number, in this case a “5”, the quartile is the average of the value at location “5” and the next number which is the value at location “6”.
The value at location 5 is “9” from the dataset.
The value at location 6 is “11” from the dataset.
Then take the average:
The median is (9 + 11) / 2 = 10
Above 10 are 50% of the data values and below 10 are 50% of the data values.
So “10” is both the median and the Q2 (because Q2 and median are the same)
1, 3, 5, 7, 9, 11, 13, 15, 17, 19
NEXT Finding Q3 (75%)
Find the 75% percentile
Use the same process.
75% percentile requires 75% or .75 of the value below.
Multiply .75 times the number of data values you have
.75 * 10 = 7.5
This is not a whole value, it is a decimal. Therefore, Q3 (also known as the 75th percentile) is the datavalue that is at the location you get when you round up. SO, “7.5” rounded UP is 8.
This means that the value in the dataset at location 8 is the Q3 (or 75th percentile).
1, 3, 5, 7, 9, 11, 13, 15, 17, 19
Q3 = 15
Q4 = max = 19