Unit 3 Notes ­ Day 2 ­ Boxplots with Outliers, Empirical Rule.notebook

1

September 30, 2013

Box and Whiskers with Outliers

Outlier: An extremely high or an extremely low value in the data set when compared with the rest of the values.

The IQR (interquartile range) is used to identify outliers.

There can be NO outliers, one outlier, or more than one outlier.

Steps to Finding the Outliers:1. Find Q1 and Q3

2. Find the IQR

3. Find Q1 - 1.5(IQR) - Low Boundary #

4. Find Q3 + 1.5(IQR) - High Boundary #

5. Check for numbers outside of this range of numbers

Example 1: Check for outliers.

2 7 8 8 9 10 12 14

The 5-number summary:

Check for a low outlier:

Q1 - 1.5(IQR) = 7.5 - 5.25 = 2.25

This is the absolute lowest value that I can accept in my set. Anything below 2.25 would be an outlier.

2 7 8 8 9 10 12 14

Check for a high outlier.

Q3 + 1.5(IQR) = 11 + 1.5(3.5) = 16.25

This is the absolute highest value that I can accept in my set.

2 7 8 8 9 10 12 14

Example 2: Check the following set for outliers.

5 6 12 13 15 18 22 50

Unit 3 Notes ­ Day 2 ­ Boxplots with Outliers, Empirical Rule.notebook

2

September 30, 2013

Letting the calculator draw the box plot for us.

3 8 15 20 22 23 24 28 29

29 30 35 38 46

Press 2nd y=

Hit enter to go to plot one and make sure it is on.

Highlight the 4th graph.

Set x-list for L1

Set frequency to 1

Press zoom 9

To read numbers press trace and use the cursor keys

Now check for outliers using the calculators.

The outliers will be shown as separate boxes.

Example: Draw the box plot (with outliers) and name the outliers).

9 12 15 27 33 45 63 72

Example: Draw the box plot (with outliers) and name the outliers.

400 506 511 514 517 521

Empirical Rule:

Normal Distribution models give us an idea of how extreme a value is by telling us how likely it is to find one that far from the mean.

We need one simple rule - The Empirical Rule - or the 68-95-99.7 Rule.

It turns out that:

Unit 3 Notes ­ Day 2 ­ Boxplots with Outliers, Empirical Rule.notebook

3

September 30, 2013

Empirical Rule:

You can only use when the variable is normally distributed.

Most values are within 3 standard deviations of the mean.

Memorize: St. Dev %1 68%2 95%3 99.70%

Example: In a normal distribution, 95% of the data will fall between what two values if:

Using the empirical rule, 95% is within 2 st. dev.

Mean - 2 St.Dev: 18 - 2(5) = 18 - 4.5 = 8

Mean + 3 St.Dev: 18 + 2(5) = 28

Range: 8 - 28

St. Dev %1 68%2 95%3 99.70%

Example: In a normal distribution, 99.7 % of the data will fall between what 2 values if:

St. Dev %1 68%2 95%3 99.70%

Example (you try):

In a normal distribution, 68% of the data will fall between what 2 values if:

St. Dev %1 68%2 95%3 99.70%

Finding the Percentage:

The mean value of a distribution is 70 and the st. dev. is 5. What % of the values fall between:

a. 60 and 80

2 standard deviations = 95%

b. 65 and 75

1 standard deviation = 68%

Example (you try): The mean value of a distribution is 70 and the st. dev. is 5. What % of the values fall between 55 and 85?