# Probability and Statistics for Engineering and the Sciences (with Student Suite Online)

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Winter, 2008 Thursday, Jan. 10 Stat 321 – Lecture 3 Descriptive Statistics cont. (Ch. 1) Numerical Summaries: Spread Range = max - min Fourth spread = f s = upper fourth – lower fourth, width of middle 50% of observations Standard deviation = 1 ) ( 2 - - = n x x s i , roughly “average deviation from mean” Example 1: Consider the following six histograms of (hypothetical) quiz scores in six classes (scores are integers ranging from 1 to 9): (a) Predict: Which has the least variability? A B C Which has the most variability? A B C Which has more variability? C D Which has more variability? D E Does class F has a lot or a small amount of variability compared to the other classes?

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Winter, 2008 Thursday, Jan. 10 (b) Determine the fourth spread of the quiz scores for each class by hand. Based on these calculations, do you need to revise any of your predictions? Class A Class B Class C Class D Class E Class F f L f U f s = f U - f L Based on these calculations, do you need to re-think any of your answers above? Explain. (c) You will be told the standard deviation of quiz scores for each class. Class A Class B Class C Class D Class E Class F Std. dev.
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