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Factoring Quadratics Factorial of a Number Bearings Area of a Triangle 1 Simultaneous Linear Equations Straight Line Graph/Graphing Linear Inequalities Area of a CylinderRange, Quartiles

Before learning how to construct a Box and Whisker plot, it's important to understand the range and quartiles of a data set of values.

The Range of a set of values, is the highest value, minus the lowest value in the set.

So it's a measure of how big a set of values range, from lowest to highest.

For example, we can have the heights of a group of **8** people.

Range =

The group of heights have a range of **17cm**.

This method works just fine when negative numbers are involved also.

Looking at a random list of  8 numbers.

Range =

A list of data values in the correct order, from lowest value to highest vakue.

Can be split up into quarters, the values where these splits take place are called "Quartiles".

Consider a random list of  10 different numbers from **42** to **68**.

Now we can look to split this ordered list of  10 numbers into **4** quarters.

The quarters of a data set are separated by Quartiles, each Quartile position can be defined in the
following way.

For a set of **n** values, each Quartile place is:

Our list is a set of  10 values, so **n** = **10**.

**2.75** is closest to **3rd** place, so rounds up to represent the
**3rd** term in the set.

**5.5** will not get rounded up or down, this number represents the middle
in between the **5th** and **6th** terms.

**8.25** is closest to **8th** place, so we round down to represent the
**8th** term in the set.

__Q1__ is called the Lower Quartile, **55**.

__Q2__ is the Middle Quartile, which is called the Median of the list.

Any time a Quartile is between  2 numbers of the list, we add each of those numbers
together and divide by **2**.

\\boldsymbol{\\frac{56 \\space + \\space 61}{2}} = \\boldsymbol{\\frac{117}{2}} =

Find the lower quartile, median and upper quartile

of the following list of  9 values.

Position **2.5** is between the  2nd and  3rd values.

Position **5** is the  5th value in the list.

Position **7.5** is between the  7th and  8th values.

Lower Quartile = \\boldsymbol{\\frac{2 \\space + \\space 4}{2}} =

Median =

Upper Quartile = \\boldsymbol{\\frac{8 \\space + \\space 8}{2}} =

The Interquartile Range is quite similar to the range of a list of values.

The Interquartile Range is the Upper Quartile, minus the Lower Quartile.

With the list of 9 numbers in Example (1.1) above:

Upper Quartile =

Interquartile Range =

A list of values with quartiles can be illustrated with what is known as a Box and Whisker Plot,
sometimes referred to as just a Box Plot.

They have the general form:

The middle part of the diagram is called the Box, with the horizontal lines and end points at each
side referred to as the whiskers.

Hence the name Box and Whisker plot.

We can represent the list of nine numbers from Example (1.1) in such a Box Plot.

LEAST VALUE =

LOWER QUARTILE =

MEDIAN =

UPPER QUARTILE =

HIGHEST VALUE =

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