Download Alg2 Notes 8.1.notebook

Alg2 Notes 8.1.notebook
March 01, 2013
8­1 Measures of Central Tendency & Variation
1. Find measures of central tendency 2. Find measures of variation
3. Find expected value
Game Theory, Airplane Seats,...
I. Measures of Central Tendency Mean: add, then divide by the number of things
Median: middle, once ordered
Mode: most frequent
1. Which class is better?
Period A's test scores: 65, 75, 65, 94, 94, 80, 75, 79, 70, 92, 90
Period B's test scores:
90, 99, 20, 80, 88, 86, 95, 75, 86, 85, 70
Period A in order: 65, 65, 70, 75, 75, 79, 80, 90, 92, 94, 94
Mean: 879/11 = 79.9
Median = 79
Mode = 65, 75, 94
Period B in order:
20, 70, 75, 80, 85, 86, 86, 88, 90, 95, 99
Mean: 874/11 = 79.45
Median = 86
Mode = 86
Alg2 Notes 8.1.notebook
March 01, 2013
2. Find the mean, median, mode for the following data. Deer at a feeder each hour: 3, 0, 2, 0, 1, 2, 4
II. Expected Value
Expected Value is the weighted average of the possible outcomes. The weight for each outcome is its probability. The probability distribution for an experiment is the function that pairs each outcome with its probability.
3. Calculating a Weighted Average
4. Calculating Expected Value
The probability distribution of successful free throws for a practice set is given below. Find the expected number of successes for one set.
The expected number of successful free throws is 2.05.
Alg2 Notes 8.1.notebook
March 01, 2013
III. Box­and­Whisker Plots
6. Make a Box­and­Whisker Plot for the classes.
Period A in order: 65, 65, 70, 75, 75, 79, 80, 90, 92, 94, 94
Period B in order:
20, 70, 75, 80, 85, 86, 86, 88, 90, 95, 99
Alg2 Notes 8.1.notebook
March 01, 2013
7. Make a box­and­whisker plot of the data. Find the interquartile range. {6, 8, 7, 5, 10, 6, 9, 8, 4}
IV. Variance & Standard Deviation
A measure of variation is a value that describes the spread of a data set. The most commonly used measures of variation are the range, the interquartile range, the variance, and the standard deviation.
Period A's test scores: Range:
65, 75, 65, 94, 94, 80, 75, 79, 70, 92, 90 IQR:
Period B's test scores:
90, 99, 20, 80, 88, 86, 95, 75, 86, 85, 70 Range:
IQR:
The variance, denoted by σ2, is the average of the squared differences from the mean. Standard deviation, denoted by σ, is the square root of the variance and is one of the most common and useful measures of variation.
Period A:
=10.604
Variance ≈ 112.44
Standard Deviation ≈ 10.604
=20.3798
Variance ≈ 415.336
Standard Deviation ≈ 20.3798
Period B:
Alg2 Notes 8.1.notebook
March 01, 2013
8. Find the mean and standard deviation for the data set of the number of people getting on and off a bus for several stops. {6, 8, 7, 5, 10, 6, 9, 8, 4}
V. Analysis
An outlier is an extreme value that is much less than or much greater than the other data values. One way: outlier > 3 standard deviations from mean
–
Another: Q1 1.5(IQR) or
Q3 + 1.5(IQR)
Analyzing effects of outliers can be useful. For example:
9. In the 2003­2004 American League Championship Series, the New York Yankees scored the following numbers of runs against the Boston Red Sox: 2, 6, 4, 2, 4, 6, 6, 10, 3, 19, 4, 4, 2, 3. Identify the outlier, and describe how it affects the mean and standard deviation.
Alg2 Notes 8.1.notebook
March 01, 2013
Oh yeah, did I mention you can do this on a graphing calculator?
8.1 p.547 #2, 5, 7, 11, 12, 16, 21, 23 ­ 25, 27, 29, 31, 36, 41, 43, 44
Extra Credit: What is the expected value of the sum of two cubes? Hint, look at #39