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### Course: Statistics and probability > Unit 3

Lesson 3: Interquartile range (IQR)# Interquartile range review

## Interquartile Range (IQR)

Interquartile range is the amount of spread in the middle $50\mathrm{\%}$ of a dataset.

In other words, it is the distance between the first quartile $({\text{Q}}_{1})$ and the third quartile $({\text{Q}}_{3})$ .

Here's how to find the IQR:

**Step 1:**Put the data in order from least to greatest.

**Step 2:**Find the median. If the number of data points is odd, the median is the middle data point. If the number of data points is even, the median is the average of the middle two data points.

**Step 3:**Find the first quartile

**Step 4:**Find the third quartile

**Step 5:**Calculate IQR by subtracting

### Example

Essays in Ms. Fenchel's class are scored on a $6$ point scale.

**Find the IQR of these scores:**

**Step 1:**The data is already in order.

**Step 2:**Find the median. There are

The median is $4$ .

**Step 3:**Find

There is an even number of data points to the left of the median, so we need the average of the middle two data points.

The first quartile is $3$ .

**Step 4:**Find

There is an even number of data points to the right of the median, so we need the average of the middle two data points.

The third quartile is $5$ .

**Step 5:**Calculate the IQR.

**The IQR is**$2$ points.

Want to learn more about calculating IQR? Check out this video.

### Practice problem

Want to practice more problems like these? Check out this exercise on interquartile range (IQR).

## Want to join the conversation?

- wait what? when will we ever use this irl?(28 votes)
- never, so idk why we need to learn this :')(13 votes)

- what if there are two numbers in the middle?(7 votes)
- it's just the first number with a '.5' so its like half. Like if the two numbers was 13,14 its 13.5

Or what ever number in in the middle of them like 13,15 then its 14. :)(9 votes)

- why do i need to know this?(6 votes)
- Interquartile range is useful when analyzing data. For example, let 50, 100, 200, 300, 400 be 5 people's money before they work, and 100, 100, 200, 350, 700 be those 5 people after they work. Now if you want to claim that at least 50% of those people has their money increased, you can use interquartile range to evaluate the correctness of this claim.(19 votes)

- the only thing teachers teach is how to be a teacher 💀(11 votes)
- Hey people. You may not be interested but I just took down a bunch of vapers in my school!(12 votes)
- You are my hero <3(2 votes)

- how can you find the median(7 votes)
- The median is simply the middle number in the data set (if you have your data set ordered from least to greatest). This is easy if you have an odd number of data.

If your number set has an even amount of data, then there's no central number. You would then take the average (or mean) of the two middle numbers to obtain the median for the data set.

Someone else gave an example of 1,2,2,3,5. Since there are an odd number of data, the median would simply be the (third) middle number of '2'.

Had the data set looked like this (with an even number of data)-

1,2,2,3,5,9

...then you would take the middle two number, and find the average (mean) of them. In this case, 2 & 3, the median would be 2+3, divided by 2, which would be 2.5.(8 votes)

- why is it called "quartile" when there're only 2 parts? I'm not a native so it's a bit confusing to me(7 votes)
- there are 4 quartiles in total, namely Q1,Q2,Q3,Q4. Below Q1 lies 25% of the data, below Q2 lies 50% of the data(Q2 is also the median of the data), below Q3 lies 75% of the data and below Q4 lies 100% of the data. So, IQR = q3 - q1, 75% - 25%, i.e 50%(4 votes)

- khan ingtrquartile range is very fun to do. Thanks(10 votes)
- you spelled it wrong(2 votes)

- guys i forgot to take my fish on a walk today(8 votes)
- um. what does that have to to with math?(5 votes)