Box-and-Whisker Plots

Emily Billoch, Isabela FernandezSebastian Pinto, Robert FridelP.5

What is a box-and-whisker plot graph?

A graph that summarizes a set of data by displaying it along a number line.

Three Parts :

A box

2 whiskers

Vocabulary

QuartilesYou have three points: the first middle point (the median), and the middle points of the two halves (what I call the "sub-medians"). These three points divide the entire data set into quarters, called "quartiles". The top point of each quartile has a name, being a "Q" followed by the number of the quarter. So the top point of the first quarter of the data points is "Q1", and so forth. Note that Q1 is also the middle number for the first half of the list, Q2 is also the middle number for the whole list, Q3 is the middle number for the second half of the list, and Q4 is the largest value in the list.

Interquartile Range

In other words, the IQR is the 1st quartile subtracted from the 3rd quartile; these quartiles can be clearly seen on a box plot on the data. It is a trimmed estimator, defined as the 25% trimmed mid-range, and is the most significant basic robust measure of scale.

8-4=4

Percentile & Percentile Rank

A percentile rank is the percentage of scores that fall at or below a given score. Definition 2: A percentile is a measure that tells us what percent of the total frequency scored below that measure. A percentile rank is the percentage of scores that fall below a given score.

STEP 1

Arrange the date in order from least to greatest.

Example:

125, 80, 140, 135, 126, 140, 350, 75

75, 80, 125, 126, 135, 140, 140, 350

STEP 2

Find the minimum, maximum, and median.

Example:

Median(Q2) = 126 +135 =130.5

The minimum is 75. The maximum is 350. The median is 130.5.

2

STEP 3

Find the first quartile and the third quartile.

75, 80, 125, 126, 135, 140, 140, 350

First quartile (Q1) = 80+125= 102.5

Third Quartile (Q3) = 140+140 = 140

The first quartile is 102.5. The third quartile is 140.

2

2

Try it yourself!

1) 12, 10, 11, 7, 9, 10, 5

Organize from least to greatest.

5, 7, 9, 10, 10, 11, 12

Find the minimum, maximum and median.

5, 7, 9, 10, 10, 11, 12

Minimum= 5

Median=10

Maximum=12

Find the first and third quartile.

Q1= 7, 9 7+9 = 8

Q3= 10, 11 10+11= 10.5

The first quartile is 8, the third quartile is 10.5 .

2

2

Example 1

101, 100, 100, 105, 101, 102, 104

Example 2

21, 34, 20, 8, 15, 29, 52, 33

Example 3

100, 72, 89, 88, 175, 120, 110, 99