AP Statistics September 9, 2008 CASA Section 1.2 Part 1 AP Statistics September 9, 2008 CASA

Describing Distributions with Numbers: Center/Mean The Mean The Average The Arithmetical Mean The mean is not a resistance measure of center AP Statistics, Section 1.2, Part 1

Describing Distributions with Numbers: Center/Median When numbers are ordered from low to high, the median is the middle number (if n is odd) or the average of the two middle numbers (if n is even) Resistant measure of center AP Statistics, Section 1.2, Part 1

Describing Distributions with Numbers: Spread/IQR The first quartile (Q1) is the median of the first half of the distribution The third quartile (Q3) is the median of the second half of the distribution The interquartile range (IQR) is the distance between the first and third quartiles. (IQR = Q3 – Q1) AP Statistics, Section 1.2, Part 1

AP Statistics, Section 1.2, Part 1 Finding M, Q1, Q3, IQR Barry Bonds’ home run counts per season (average=35.4): 16, 19, 24, 25, 25, 33, 33, 34, 34, 37, 37, 40, 42, 46, 49, 73 Hank Aaron’s home run counts per season (average=34.9): 13, 20, 24, 26, 27, 29, 30, 32, 34, 34, 38, 39, 39, 40, 40, 44, 44, 44, 44, 45, 47 AP Statistics, Section 1.2, Part 1

AP Statistics, Section 1.2, Part 1 Finding M, Q1, Q3, IQR Barry Bonds: Q1=25, M=34, Q3=41, IQR=16 Hank Aaron: Q1=28, M=38, Q3=44, IQR=16 What does this say about comparing Bonds and Aaron? AP Statistics, Section 1.2, Part 1

Describing Distributions with Numbers: Outliers If a data point is greater than Q3 +1.5 * IQR or If a data point is less than Q1 - 1.5 * IQR . Barry Bonds: M=34, Q1=25, Q3=41, IQR=16 41 + 1.5 * 16 = 65 (anything above 65) 25 - 1.5 * 16 = 1 (anything below 1) AP Statistics, Section 1.2, Part 1

Describing Distributions with Numbers: 5 Number Summary We can summarize a distribution (a data set) with 5 numbers Minimum Q1 Median Q3 Maximum AP Statistics, Section 1.2, Part 1

AP Statistics, Section 1.2, Part 1 Boxplot AP Statistics, Section 1.2, Part 1

AP Statistics, Section 1.2, Part 1 Modified Boxplot AP Statistics, Section 1.2, Part 1

AP Statistics, Section 1.2, Part 1 Assignment Exercises 1.31 – 1.39, The Practice of Statistics. AP Statistics, Section 1.2, Part 1