Chapter 6-The Standard Deviation as aRuler and the Normal Model

Chapter 6-The Standard Deviation as aRuler and the Normal Model

1. Standardizing

   • A value found by subtracting the mean and dividing by the standard deviation.

2. Shifting

   • Adding a constant to each data value adds the same constant to the mean, the median, and the quartiles, but does not change the standard deviation or IQR.

3. Rescaling

   • Multiplying each data value by a constant multiplies both the measures of position (mean, median, and quartiles) and the measures of spread (standard deviation and IQR) by that constant.

4. Parameter

   • A numerically valued attribute of a model.

5. Statistic

   • A value calculated from data to summarize aspects of the data

6. z-score

   • A z-score tells how many standard deviations a value is from the mean; z-scores have a mean of 0 and a standard deviation of 1.

7. 68–95–99.7 Rule

   • In a Normal model, about 68% of values fall within 1 standard deviation of the mean, about 95% fall within 2 standard deviations of the mean, and about 99.7% fall within 3 standard devia- tions of the mean.