Homework: pg. 82 #33, 35, 36, 38 33.) B. Women: 101, 126, 138.50, 154, 200 Men: 70, 95, 114.5, 144.5, 187 C. Women generally score higher than men, All five statistics are higher for women. The men’s scores are more spread out than the women’s. The shapes are similar, both slightly skewed right.

35.) yes, IQR is a resistant measure of spread. For example: 1,2,3,4,5. The IQR is 2 even if the 5 changes to a 100. 36.) A. $1735 Outliers: 85.76, 86.37, and 93.37.

38.) A. 5.7%, 11.675%, 12.75%, 13.5%, and 17.6% B. It would flag Alaska, Florida, and the one with 8.5%.

1.2 Standard Deviation

Variance variance—average of the squares of the deviations of the observations(data values) from their mean

Standard Deviation standard deviation—measures the spread of data s is the typical distance (deviation) around the mean

Find the standard deviation and variance Amount of Substance in French Fries 497 193 328 155 326 245 270

Properties of Standard Deviation s=0 when… there is NO SPREAD/VARIABLILITY This happens only when all observations have the same value As observations become more spread out about their mean, s gets larger s is not resistant—few outliers can make s very large

To describe Distributions: Symmetric Distributions: Use mean(x-bar) and standard deviation(s) Skewed Distributions: Use median and IQR

What happens when data changes? Fathom Demo What happens when data changes?

To summarize: Multiplying each observation by a positive number b multiples both measures of center (mean and median) and measures of spread (IQR and standard deviation). Adding the same number a (either positive, zero, or negative) to each observation adds a to measures of center but DOES NOT CHANGE measures of spread.

Examples: Explain how these affect mean, median, IQR, and standard deviation You collect data on the power of car engines, measured in horsepower. Your teacher requires you to convert power to watts. One horsepower is 746 watts. You measure temperature in Fahrenheit and you need to convert to Celsius (F=9/5C+32) Your teacher gave you a hard test and wants to “curve” it. She adds 10 points to each student’s score.

HW: pg 89 #39, 40, 42, 43