**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 75^{th} 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 75^{th} percentile).

1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Q3 = 15

Q4 = max = 19