# Probability and Statistics

### Topics

## Introduction to :

The phrase "a la mode," used today to mean "with ice cream," literally means "in the fashion." As we know, there is nothing more fashionable than ice cream. In statistics, the **mode** of a set of data is the most frequently occurring value. In other words, the mode is the most fashionable value. You can wear it around your neck as a wrap, or as a hat. It's incredibly versatile.

### Sample Problem

The colors of ten students' backpacks are recorded. Who knows why, but apparently someone thinks it's important.

black, blue, red, blue, green, blue, black, orange, blue, blue.

What is the most fashionable backpack color?

Putting your personal preference aside, the most fashionable backpack color is blue, since more students have a blue backpack than any other color. In more mathematical terms, blue is the mode of this set of data. However, by the time autumn rolls around, blue is going to be out and orange is totally going to be in.

### Samples

In the list of values

12, 13, 13, 13, 14, 15, 16, 16, 16, 17, 17

there are two modes: 13 and 16. The numbers 13 and 16 each occur three times, which is more than any of the other numbers. Therefore, 13 and 16 are both fashionable. Explains why the two of them are so cliquish.

The list of values

50, 60, 70, 80, 90

has no mode. Since each number occurs only once, there are no "fashionable" numbers in this list. Still, it wouldn't hurt you to be civil to them.

**Be careful:** 0 is a perfectly good number, and a perfectly good mode. Having a mode of 0 is different from having no mode at all.

#### Example 1

The students' test scores are 77, 80, 77, 64, 50, 84, 90, 77. What is the mode of the test scores? |

#### Example 2

The high temperatures in a very cold town in Canada over one week were -20, 0, -5, 0, 0, 1, 0. |

#### Exercise 1

Find the mode(s), if any, for the following set of data. It may be helpful to order the data first.

80, 82, 94, 76, 54, 60, 89, 88, 82, 97.

#### Exercise 2

Find the mode(s), if any, for the following set of data. It may be helpful to order the data first.

green, red, blue, red, black, green, black, purple, orange.

#### Exercise 3

Find the mode(s), if any, for the following set of data. It may be helpful to order the data first.

3.14, 2, 5, 6, 7, 4, 9, 0, 1.

#### Exercise 4

Find the mode(s), if any, for the following set of data. It may be helpful to order the data first.

4, 5, 2, 8, 2, 1, 0, 0, 9, 5, 0.

#### Exercise 5

Find the mode(s), if any, for the following set of data. It may be helpful to order the data first.

cat, dog, parakeet, cat, llama, duck, fish, zebra, giraffe, cat, llama