Warm Up Complete the warm up Ms Kennedy

Measures of Spread • Differences in spread can influence interpretation of the data set

Variability • Variability = Consistency • How consistent are the measurements? • Consider the

Range • Range = Largest Value – Smallest Value • Crude measure of spread

Standard Deviation • Distance each data value is from the mean • Standard deviation

Connie’s test scores Oscar’s test scores • • • 82, 84, 85, 86 Mean

So far… We have been identifying outliers just by what we assume sticks out

To find outliers, we use 1. 5 IQR Rule 1 st: Find the IQR

Example 1: • Calculate the IQR from the data set below 87, 7, 41,

You can also find if you have outliers in your calculator by creating a

Example 2 Using your calculator identify the outlier, if there is one 59, 27,

Example 3: Now add a 150 to the last data set and see what

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Warm Up Complete the warm up Ms. Kennedy handed to you on your way into class.

Quiz!! You have 20 minutes!!

Measures of Spread And Outliers

Measures of Spread • Differences in spread can influence interpretation of the data set • Range is a crude measure of spread • Other measures of spread: –Variance –Standard Deviation

Variability • Variability = Consistency • How consistent are the measurements? • Consider the following data sets: 24, 25, 25, 26 1, 2, 3, 47, 48, 49 • Both data sets have a mean & median of 25, but the sets are very different

Range • Range = Largest Value – Smallest Value • Crude measure of spread • Affected by outliers

Standard Deviation • Distance each data value is from the mean • Standard deviation formula is complicated: Use the calculator to compute standard deviation • Find the standard deviation for the following data: 3, 4, 5, 6, 4, 2, 0, 8, 4 Grab a calculator! Same steps as yesterday we are just looking at a different symbol, Sx.

Connie’s test scores Oscar’s test scores • • • 82, 84, 85, 86 Mean – Median – Mode – Range – Standard Deviation - • • • 72, 76, 84, 90, 94, 96 Mean – Median – Mode – Range – Standard Deviation – Which student is more consistent?

So far… We have been identifying outliers just by what we assume sticks out from the group, but we all know what happens when you assume so now lets use a formula.

To find outliers, we use 1. 5 IQR Rule 1 st: Find the IQR = Q 1 – Q 3 2 nd: Multiply your IQR by 1. 5 3 rd: Identify your limits (any value outside of these limits is an outlier) • Lower limit = Q 1 – (your value from step 2) • Upper limit = Q 3 + (your value from step 2)

Example 1: • Calculate the IQR from the data set below 87, 7, 41, 50, 15, 220, 23, 99, 11, 45, 11, 61, 3, 39, 21

You can also find if you have outliers in your calculator by creating a box plot. Step 1: Type data into L 1 Step 2: Turn your box plot on (1 st option) - 2 nd y= Enter (on, and 4 th option highlighted) Step 3: Look at the box plot - Zoom 9: Zoom. Stat

Example 2 Using your calculator identify the outlier, if there is one 59, 27, 18, 78, 61, 91, 52, 34, 54, 93, 100, 87, 85, 82, 68

Example 3: Now add a 150 to the last data set and see what your box plot looks like.