Chapter 3-4: Measures of Relative Standing

Assignments and due dates for each chapter are announced in class. Typical problems include:

3-2 page 86

2 to 24, even numbered problems

Do not calculate the mode or the midrange since we will not use either of these measures.

3-3 page 104

2 to 24, even numbered problems

Do not use formulas 3-4 or 3-5 (page 94) to compute the standard deviation. Use STATDISK or a calculator's built-in functions or a spreadsheet's built-in functions to compute the standard deviation.

3-4 page 116

2 to 14, even numbered problems

3-5 page 126

2 to 12, even numbered problems

Chapter 3-4: Measures of Relative Standing

The mean and standard deviation can be used to compute z (or z-score), a measure of the relative standing of an item within the distribution.

Use the formulas on page 110 to compute z. Always round z to at least 2 decimal places, sometimes 3 decimal places.

Important points.
1. z is exactly the number of standard deviations a particular value (x) is separated from the the mean.
2. Data (x values) larger than the mean always produce positive z scores. Data (x values) less than the mean always produce negative z scores.
3. Figure 3-5 on page 111 introduces an important technique.

First statisticians define (quite arbitrarily) the ranges of "usual" and "unusual"; in this case anything that happens less than 5% of the time is "unusual" and anything that happens more than 5% of the time (e.g. the other 95% of the time) is "usual".

Second, staticians make calculations (which are not arbitrary) to determine if particular events are "usual" or "unusual".