5 Number Summary, Boxplots, Outliers, and Resistance

5 Number Summary on the TI Graphing Calculator

Graph Box and Whisker on the TI Graphing Calculator… To graph box and whisker … 2 ND Y = 1: PLOT 1…ON ON (should be highlighted if not push ENTER) TYPE: (arrow over 4 times) ENTER GRAPH **If graph does not show up, ZOOM 9: STAT

Mean Bill Gates makes $500 million a year. He ’ s in a room with 9 teachers, 4 of whom make $40k, 3 make $45k, and 2 make $55k a year. What is the mean salary of everyone in the room? What would be the mean salary if Gates wasn ’ t included? Mean With Gates: $50,040,500 Mean Without Gates: $45,000

Resistance The mean is a non-resistant measurement, which means that extreme values will pull it towards that end of the data. The median is a resistant measurement. Extreme values have no affect on it. Note- If the mean and median are the same then the dist. is roughly symmetric. Mean smaller-skewed left, mean larger-skewed right

5 Number Summary/Boxplot

Example: Ages of actresses at the time they first won the Oscar

Box Plot We need 5 numbers, called the 5 number summary: 1. minimum value 2. Q1 (median of 1 st half) 3. median 4. Q3 (median of 2 nd half) 5. maximum value

Calculate the 5 number summary for actresses data Min = 21 Q1 = 30 Med = 34 Q3 = 41 Max = 80 Construct a boxplot for the 5 number summary

1. If the median is near the center of the box and each of the horizontal lines (“whiskers”) are approximately equal length, then the distribution is roughly symmetric. 2. If the median is left of the center of the box and/or the right “whisker” is substantially longer than the left line, the distribution is right skewed. 3. If the median is right of the center of the box and/or the left line is substantially longer than the right line, the distribution is left skewed. Distribution Shape Based Upon Boxplot

Symmetric

Skewed Right

Skewed Left

In a set of numbers, a number that is much LARGER or much SMALLER than the rest of the numbers is called an Outlier.

Criteria for Outliers Remember that an outlier is a data value that lies very far away from the majority of all the other data values in the data set. The following is criteria to identify outliers in a data set. The inter-quartile range (IQR) is the value of Q3 – Q1 x is an outlier if of one the following inequalities is true: 1. x > Q x IQR 2.x < Q x IQR Does our data have any outliers?

Box plot with outliers (Modified Boxplot) When we select the 1 st box plot on the TI, it allows us to see outliers. Select the mark that is visible for you.

Trace and go to the right twice. The 50 is the last data value that is not an outlier.

Homework 1.26, 29, 31-34,36-39