Quartiles

Quartiles are the values that divide a list of numbers into quarters:

  • Put the listing of numbers in order
  • And so cutting the listing into four equal parts
  • The Quartiles are at the "cuts"

Like this:

Example: 5, vii, 4, 4, vi, 2, 8

Put them in club: ii, 4, 4, 5, half dozen, 7, 8

Cut the list into quarters:

Quartiles of 2, 4, 4, 5, 6, 7, 8

And the outcome is:

  • Quartile 1 (Q1) = iv
  • Quartile 2 (Q2), which is also the Median, = v
  • Quartile 3 (Q3) = 7

Sometimes a "cut" is betwixt two numbers ... the Quartile is the average of the two numbers.

Example: 1, 3, iii, 4, 5, six, 6, seven, viii, viii

The numbers are already in order

Cut the list into quarters:

Quartiles

In this case Quartile two is one-half way betwixt v and 6:

Q2 = (5+6)/2 = 5.five

And the result is:

  • Quartile i (Q1) = 3
  • Quartile 2 (Q2) = 5.5
  • Quartile 3 (Q3) = 7

Interquartile Range

The "Interquartile Range" is from Q1 to Q3:

Interquartile Range

To calculate it just subtract Quartile 1 from Quartile 3, similar this:

Example:

Quartiles of 2, 4, 4, 5, 6, 7, 8

The Interquartile Range is:

Q3 − Q1 = 7 − 4 = three

Box and Whisker Plot

We can testify all the of import values in a "Box and Whisker Plot", like this:

Box and Whisker Plot

A final example covering everything:

Example: Box and Whisker Plot and Interquartile Range for

iv, 17, seven, 14, xviii, 12, 3, 16, ten, 4, 4, 11

Put them in order:

iii, 4, four, 4, 7, 10, xi, 12, 14, 16, 17, 18

Cut it into quarters:

3, 4, four | 4, 7, 10 | 11, 12, 14 | 16, 17, eighteen

In this example all the quartiles are between numbers:

  • Quartile 1 (Q1) = (4+4)/two = four
  • Quartile 2 (Q2) = (10+11)/2 = 10.v
  • Quartile 3 (Q3) = (14+16)/2 = fifteen

Also:

  • The Everyman Value is 3,
  • The Highest Value is 18

So now we have plenty data for the Box and Whisker Plot:

box whisker plot

And the Interquartile Range is:

Q3 − Q1 = 15 − four = xi