QUARTILES

Basic Concepts

100

This measure divides a data set into four equal parts.

Quartiles

200

This quartile is also called the median.

Q₂  / Quartile 2 / 2nd Quartile

300

This quartile marks the lowest 25% of the data.

Q₁ / Quartile 1 / 1st Quartile

400

This quartile separates the top 25% of the data from the lower 75%.

Q₃ / Quartile 3 / 3rd Quartile

500

These five values make up the five-number summary.

Minimum, 1st Quartile, 2nd Quartile, 3rd Quartile and Maximum

Finding Positions

100

The formula used to find the position of Qk.

Q_k=k(n+1)/4

200

For 11 data values, this is the position of the median.

6th position

300

If n = 15, this is the position of Q1.

4th position

400

If n = 12, Q2 lies between these two positions.

6th and 7th position

500

For n = 19, this is the position of Q3.

15th position.

Computation

100

Find the median of the ordered data:
3, 5, 7, 9, 11 

7

200

Find Q1 of:
14, 2, 10, 6, 12, 4, 8

4

300

Find Q3 of:
18, 6, 21, 3, 12, 15, 9

18

400

Find the interquartile range of:
24, 8, 32, 16, 4, 36, 20, 12, 28

16

500

For the data set:
35, 10, 55, 25, 45, 15, 40, 5, 30, 50, 20

30

Box Plot & IQR

100

This graph visually displays quartiles.

box-and-whisker plot

200

This is another name for the middle 50% of the data.

interquartile range

300

This part of the box plot shows Q1 to Q3

box

400

The five-number summary of a dataset:
Min = 19, Q1 = 35, Q2 = 50, Q3 = 83, Max = 100

What is IQR? 

48

500

IQR of a dataset is 28. If Q₃ = 109, what is Q₁?

81

Interpretations

100

Q2 divides the data set into these two equal groups.

lower half and upper half

200

If your height is above Q3, you are taller than this percent of the group.

75%

300

If Q1 = 60 and Q3 = 80, this is the IQR.

20

400

A smaller IQR means the data are more this.

consistent / less spread out

500

When Q1 and Q3 are far apart, the data show this characteristic.

High variability / large spread