EQ: How is the standard deviation computed and used? Ch. 4 Day 3 AP Statistics EQ: How is the standard deviation computed and used?

Standard Deviation It measures the SPREAD of the data. Variance = (Std. Dev)² Find it on your formula sheet!!!!!!!!!

Formula 𝑆 𝑥 = 1 𝑛−1 𝑥− 𝑥 2

If many data values are scattered far from the center, the IQR and the standard deviation will be __________. If the data values are close to the center, these measure of spread will be __________. larger smaller

Squared Deviations (xi-x)² Finding Σ(xi-x)² You must show this by hand for now  Fill out the table (let your calc help you!) Observations xi Deviations xi-x Squared Deviations (xi-x)² LIST 1 LIST 2 LIST 3

Finding Standard Deviation What do you have to show? Calculate 𝑥 Fill in Σ( 𝑥 𝑖 − 𝑥 )² Let your calculator give you that value, SUM OF L3! Fill in 1 𝑛−1 Are you looking for v or s? If v, then leave alone If s, then take the square root

Find the standard deviation of the test scores of 15 employees enrolled in a CPR class: 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 𝑺 𝒙 ≈𝟕.𝟔𝟏

What does the standard deviation tell us about our data set?

Annual Number of Deaths from Tornados in the US 53 39 33 69 30 25 67 94 40 Find the standard deviation.

What Can Go Wrong? Don’t forget to do a reality check. Don’t forget to sort the values before finding the median or percentiles. Don’t compute numerical summaries of a categorical value. Watch out for multiple modes. Be aware of slightly different methods.

Beware of outliers. Make a picture!! Be careful when comparing groups that have very different spreads.

Homework P. 72 #16, 29, 30, 48