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Quartiles of Data

Q: When dividing your data set into an upper half and a lower half, what do you do with the median, do you include it? If so on which side: upper half or lower half?

Yes you include it on both sides . Given the following data set: 2, 3, 5, 7, 8, 9, 10, 12, 15 Your Q2 (median) is 8. Your lower half consists of: 2, 3, 5, 7, 8 Your upper half consists of: 8 , 9, 12, 12, 15 So its included on both halves. Btw, your Q1 = 5 and Q3 = 10 in this example.

5 important questions on Quartiles of Data

What is a big confusion point about quartiles (and therefore a pitfall you need to avoid)?

Even though quartiles sounds like quarter (hinting at the number 4) and even though they do divide the data into 4 sets, what you write down is Q1, Q2 (same as median) and q3. There is no Q4.

Can you identify how much of the data is represented by each quartile (in %)?

Q1 is greater than or equal to 25% of the data
Q2 is greater than or equal to 50% of the data
Q3 is greater than or equal to 75% of the data

Another way to state it is to say that
25% of the data lies below Q1
50% of the data lies below Q2
75% of the data lies below Q3

When dividing your data set into an upper half and a lower half, what do you do with the median, do you include it? If so on which side: upper half or lower half?

Yes you include it on both sides. Given the following data set:

2, 3, 5, 7, 8, 9, 10, 12, 15

Your Q2 (median) is 8.
Your lower half consists of: 2, 3, 5, 7, 8
Your upper half consists of: 8, 9, 12, 12, 15

So its included on both halves.
Btw, your Q1 = 5 and Q3 = 10 in this example.

If you have an odd number of data sets, your median (aka your Q2) is the middle number. How is Q2 calculated when you have an even number of data points?

Same as you would with any median; take the average of the 2 middle numbers.

If you have an odd number of data points, you include the median (aka Q2) in both the lower half and the upper half. What number do you include for each half when you have an even amount of data points?

Of the 2 middle numbers, you include the one on the left (usually the lower value) to the lower half, and the one on the right (usually the upper value) to the upper half.

Example:

2, 3, 4, 5, 6, 7

Your Q2 = 4.5
Your lower half = 2, 3, 4
Your upper half = 5, 6, 7

The question on the page originate from the summary of the following study material:

Math Tutor DVD - Probability & Statistics

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Quartiles of Data

5 important questions on Quartiles of Data

What is a big confusion point about quartiles (and therefore a pitfall you need to avoid)?

Can you identify how much of the data is represented by each quartile (in %)?

When dividing your data set into an upper half and a lower half, what do you do with the median, do you include it? If so on which side: upper half or lower half?

If you have an odd number of data sets, your median (aka your Q2) is the middle number. How is Q2 calculated when you have an even number of data points?

If you have an odd number of data points, you include the median (aka Q2) in both the lower half and the upper half. What number do you include for each half when you have an even amount of data points?

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