Define the following words in your own definition WARM UP Define the following words in your own definition Mean Median Mode Range

Define the following words in your own definition WARM UP Define the following words in your own definition Mean – the average of a set of data Median- the number that is in the middle when the data is in order Mode- the number that appears the most Range- the difference between the largest and smallest number

Box-and-Whisker Plots

Step 1 – Order Numbers 1. Order the set of numbers from least to greatest

Step 2 – Find the Median 2. Find the median. The median is the middle number. If the data has two middle numbers, find the mean of the two numbers. What is the median?

Step 3 – Upper & Lower Quartiles 3. Find the lower and upper medians or quartiles. These are the middle numbers on each side of the median. What are they?

Step 4 – Draw a Number Line Now you are ready to construct the actual box & whisker graph. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data:

Step 5 – Draw the Parts Locate the main median 12 using a vertical line just above your number line:

Step 5 – Draw the Parts Locate the lower median 8.5 and the upper median 14 with similar vertical lines:

Step 5 – Draw the Parts Next, draw a box using the lower and upper median lines as endpoints:

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

Step 6 - Label the Parts of a Box-and-Whisker Plot Lower Quartile Median Upper Quartile Lower Extreme 3 1 2 Upper Extreme 4 5 Name the parts of a Box-and-Whisker Plot

14 – 8.5 = 5.5 Interquartile Range The interquartile range is the difference between the upper quartile and the lower quartile. 14 – 8.5 = 5.5

Are There Any Outliers? Using the 1.5*IQR Rule

Say we have the following data: 1,2,5,5,7,8,10,11,11,12,15,20 Notice that you must have ordered data before you can find the Five – Number – Summaries. Find the median first. It’s the middle point. Then find the quartiles, Q1 and Q3. They are the middles of the lower and upper half, respectively. The last thing to do is determine whether there are outliers using the 1.5*IQR Rule

min Q1 Q3 max 1,2,5,5,7,8,10,11,12,12,18,25 1 5 9 12 18 25 -5.5 22.5 1.5IQR IQR = 12 – 5 = 7 1.5IQR 5 - 1.5 * 7 = -5.5 12 + 1.5 * 7 = 22.5 25 is considered an outlier and will be a point in a boxplot and the ‘whisker’ ends at the last non-outlier data point.