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

2. 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

3. 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

4. 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

5. 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

6. 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

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

8. 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

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

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

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