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Box and Whisker Graph

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Box and Whisker Graph

A box and whisker graph is used to display a set of data so that you can easily see where most of the numbers are.

For example, suppose you were to catch and measure the length of 13 fish in a lake:

12

6

12

9

14

12

5

13

8

9

14

16

20

A box and whisker plot is based on medians. The first step is to rewrite the data in order, from smallest length to largest:

6

12

12

9

14

12

5

13

8

9

14

16

20

5 6 8 9 9 12 12 12 13 14 14 16 20

8.5

14

Now find the median of all the numbers.

The next step is to find the lower median. This is the middle of the lower six numbers. The exact centre is half-way between 8 and 9 ... which would be 8.5.

Now find the upper median. This is the middle of the upper six numbers. The exact centre is half-way between 14 and 14 ... which must be 14

5 6 8 9 9 12 12 12 13 14 14 16 20

8.5

14

•

•

4 5 8 10 12 14 16 18 20 22

Next, draw a box using the lower and upper median lines as endpoints:

Finally, the whiskers extend out to the data's smallest number 5 and largest number 20:

Now locate the lower median8.5 and the upper median14 with similar vertical lines:

First, locate the main median12 using a vertical line just above your number line:

Now draw a number line

•

•

4 5 8 10 12 14 16 18 20 22

This is a box & whisker plot!

Sometimes little tricks are used to save space when creating graphs.

This means that part of the graph is missing

The problem is that these little tricks can distort our understanding of the information if we do not pay close attention to every detail of the graph.

If we were to stretch this bar graph out, the red bar and the green bar would look closer to the same height.

Fundamental Counting Principle

Most of you probably think you know how to count, and I’m inclined to agree with you, but I would like to make sure by asking you a few questions.

A deli has a lunch special which consists of a sandwich, soup, and dessert $4.99.

They offer the following choices:

Sandwich:

chicken salad, ham, tuna, and roast beef

Soup:

tomato, chicken noodle, vegetable

Dessert:

cookie and pie

How many lunch specials are there?

tomato

cookie

If you trace back each line you can see every possible combination.

chicken salad

pie

cookie

chicken noodle

pie

vegetable

cookie

pie

cookie

tomato

pie

cookie

ham

chicken noodle

pie

cookie

vegetable

Now if I traced back all the way down, I would find that I have 24 possible combinations.

pie

cookie

tomato

pie

cookie

tuna

chicken noodle

pie

cookie

vegetable

pie

cookie

tomato

pie

cookie

chicken noodle

pie

roast beef

cookie

vegetable

pie

Let’s Multiply!!

Why yes there is!!!!

Isn’t there an easier way!!!

A deli has a lunch special which consists of a sandwich, soup, and dessert $4.99.

They offer the following choices:

Sandwich:

chicken salad, ham, and tuna, and roast beef

Soup:

tomato, chicken noodle, vegetable

Dessert:

cookie and pie

4 Sandwiches • 3 Soups • 2 Desserts

4 • 3 • 2 = 24

The ATM at the bank will take up to 4 digits (including zero) for a numerical pass code. How many different pass codes can you create?

10,000 why?

0000, 0001, 0002, 0003, 0004, 0005, 0006, 0007, 0008, 0009, 0010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018,1019, …, 9988 9989, 9990, 9991, 9992, 9993, 9994, 9995, 9996, 9997, 9998, 9999

You see, if I had started with 0001, then there would be 9,999, but I stared with 0000, so there are 10,000