Chapter 3

The mean will be pulled in the direction of the

• Notes
• 88

This preview shows page 28 - 43 out of 88 pages.

The mean will be pulled in the direction of the extreme values. The Ralph Sampson story illustrates the problem.

Subscribe to view the full document.

Look at the income distribution in the USA in 1992
Asymmetric, skewed to the right The median income is marked on the graph, at about \$22,000 a year. The mean is not reported, but it appears to be about \$30,000 a year.

Subscribe to view the full document.

Many people use statistics the way a drunk uses a lamp post For support . . . Not for Illumination.
And they play games with the mean and median An incumbent politician will boast of how well the economy is doing, and use mean income numbers as evidence. The challenger will complain of how badly the economy is doing, and use median income numbers as evidence. Confusing voters.

Subscribe to view the full document.

Measures of Variability Range Interquartile Range Variance Standard Deviation Coefficient of Variation
The Range The Range of a data set is just the difference between the biggest and smallest observation. The Range is easy to compute, but it is not robust, and therefore may be misleading. As in: “Starting salaries for Rhetoric and Communications majors range from \$18,000 to \$2,000,000 a year.”

Subscribe to view the full document.

An Example Lets use the earlier data to illustrate. 2,3, 3, 4, 6, 7, 8, 11, 12, 13, 15, 16, 17 The Range is 17 2 15 =
Interquartile Range (IQR) This is the spread of the middle 50% of the observations. It is defined as Q3 – Q1 Q3 is the third quartile, or 75 th percentile. 75% of all observations are smaller than Q3. Q1 is the first quartile, or 25 th percentile. 25% of all observations are smaller than Q1. (Q2 is the second quartile, or median.)

Subscribe to view the full document.

How do you find quartiles? Basically, to find Q3, the 75 th percentile, order the data and throw away 3 observations from the bottom for every one from the top. Here, Q3 is 13. 2,3, 3, 4, 6, 7, 8, 11, 12, 13, 15, 16, 17 2 , 3 , 3, 4 , 6 , 7 , 8 , 11 , 12 ,13, 15, 16 , 17