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September 27.docx

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Department
Statistics
Course
STAT 1770
Professor
John Sheriff
Semester
Fall

Description
September 27, 2013 Chapter 5, Section 1-4; pages 110-126 Exercise 5.20 • What are their z­scores? [(y­y)/s] o Feb z= (6.73­2.324) / 1.577 = 2.79 o June = (3.93­0.857)/0.795 = 3.865 o Aug = (2.53­0.63) / 0.597 = 3.18 • Which was the most extraordinary wind event? o June Standardized Z­scores­ Shifting and Rescaling • Z= (observed value­mean)/ standard deviation o Shifting the data, by adding or subtracting a constant to each value  changes each measure of postion (mean, median, min, max, percentiles)  by the same constant  New mean= old mean +constant or new mean = old mean – constant o Shifting the data, by adding or subtracting a constant to each value has no  impact on measures of spread (range, UQR, standard deviation)  New IQR = old IQR o Rescaling the data, by multiplying or dividing each value by a constant  changes each masure of position (mean, median, min, max, percentiales)  and each measure of spread (range, IQR, standard deviation) by the same  constant  New mean = (old mean) x constant ; new mean= (old  mean)/constant  New IQR = (old IQR) x constant; new IQR = (old IQR)/ constant o Shifting and/or rescaling does not change the shape of the distribution Exercise 5.28 • What is the mean speed now? What is the new standard deviation? o Old mean = 23.84, old SD = 3.56 o Adjust each Y value (speed) by subtracting 20 (y­20) o New mean= Old mean ­20 = 23.84­20= 3.84 o New s = Old s­ 3.56mph • His friend in Berlin want to study speeds, so John converts the original mile­per­ hour readings to km/h by multiplying all speeds by 1.609. What is the mean now?  What is the new SD? o Adjust each y value by multiplying by 1.609 o Mean = 23.84 x 1.609 = 38.36 o S= 3.56 x 1.609 = 5.73 The Normal Model (Distribution) • Some distributions deserve special attention because they are useful for man
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