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### Course: 6th grade (Illustrative Mathematics)>Unit 8

Lesson 13: Lesson 15: Quartiles and interquartile range

# Interquartile range (IQR)

AP.STATS:
UNC‑1 (EU)
,
UNC‑1.J (LO)
,
UNC‑1.J.1 (EK)
,
UNC‑1.J.2 (EK)
CCSS.Math:
The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

## Want to join the conversation?

• Where is IQR used in math? Is this for only box and whisker plots?
• Its a measure of spread which is useful for data sets which are skewed.
• I have a doubt and I didn't know where else to ask because there isn't any video on Quartile Deviation.

What exactly is Quartile Deviation? From where are we calculating the deviation? For eg. In Mean Absolute Deviation we subtract Mean from each data point, add them all up and divide by the number of data points i.e we're basically calculating the average deviation of data points from the MEAN! but in Quartile Deviation we do not use that formula instead the formula is (Q3-Q1)/2. My question is why is this *(Q3-Q1)/2* the formula?

• The Quartile Deviation (QD) is the product of half of the difference between the upper and. lower quartiles. Mathematically we can define as: Quartile Deviation = (Q3 – Q1) / 2. Quartile Deviation defines the absolute measure of dispersion
• Greetings and salutations to those reading my comment I benjamin chapman require assistance to understand in what situation would one might use Interquartile range I fully grasp the concept of how to calculate with Interquartile range
but can't seem to think how where it would be appropriate to use it,if you are capable of helping me and do so I would very much appreciate you contributing the my knowledge in the subject matter,if you are unable to do so because you are in a similar position as I then I wish you the best of days in searching for the answer to your question,but for now fare well.
benjamin chapman
• As Sal said, the interquartile range gives you an idea of how far apart the data is spread out. For example if we had the data sets: (1, 1, 1, 5, 9, 9, 9) and (2, 3, 4, 5, 6, 7, 8) the median is 5 and the mean is 5 for both of them but if you find the IQR of them you see it is 8 and 4, respectively.
A more practical example of this could be the grades of a math class. The class could have an average of 75%, but that does not tell you what the spread of grades is. An IQR of 10 would mean the data isn't spread out as much as if it were 20.
• How would negative numbers or irrational numbers affect your Interquartile range (IQR)?
• The IQR would still be positive, but possibly irrational.

For example, the data set
{−√2, −1, −√3∕2, −1∕2, 0, 1, 2, 4, 5, 5√3}
would have
Q1 = −√3∕2
Q3 = 4

IQR = Q3 − Q1 = 4 − (−√3∕2) = (8 + √3)∕2
• why do we need Interquartile range? I mean where do we use them?
• In a word statistics. In statistical jobs you want to understand the data as thoroughly as possible, so you want as many ways to get an idea of its pattern. IQR is one of those ways.
• this is hard for me
• also what are median mean? dose some one have a song or a riddle etc. to help remeber it maby?
• median is the middle, idk why but ive always remembered it as middle cause to me median kinda sounds like middle...for whatever reason
• how does he draw with his mouse so perfectly
• So, in this video Sal writes out the number each dot represents. However, Sal does not simply by multiplying if he has multiple number. For example at in the video, Sal had 2 9s and did not write 18, 9x2. Could you do this. Just curious. :)
• You should not add repeated numbers together; this would change the value of the median, quartiles, and the IQR. Using the example from the video,

The median of 7, 9, 9, 10, 10, 10, 11, 12, 12, 14 is 10. Q1 = 9, and Q3 = 12, making the IQR = 3.

Now, adding all the multiple numbers together would get us 7, 9 + 9, 10 + 10 + 10, 11, 12 + 12, 14; or 7, 18, 30, 11, 24, 14.

Before we can find the median, we need to arrange the numbers from smallest to largest: 7, 11, 14, 18, 24, 30

The median of this set is 16. Q1 = 11 and Q3 = 24, making the IQR = 13.

Hope this clears things up!😄