Chapter 6: The Standard Deviation as a Rule and the Normal Model Flashcards
Define ‘Standardizing’.
We standardize to eliminate units. Standardized values can be compared and combined even if the original variables had different units and magnitudes.
Define ‘Standardized values’.
A value found by subtracting the mean and dividing by the standard deviation.
Define ‘Z-score’.
A z-score tells how many standard deviations a value is from the mean; z-scores have a mean of zero and a standard deviation of one. When working with data, use the statistics y and s:
z=(y - y-bar) / s
When working with models, use the parameters (Greek) μ and σ:
z=(y - μ) / σ
Define ‘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 the IQR.
Define ‘Rescaling’.
Multiplying each data value by a constant multiplies both the measure of position (mean, median, and quartiles) and the measures of spread (standard deviation and IQR) by that constant.
Define ‘Density curve’.
A model for the frequency distribution of data using areas under the curve to represent relative frequencies.
Define ‘Parameter’.
A numerically valued attribute of a model. For example, the values μ and σ in a N(μ, σ) model are parameters.
Define ‘Statistic’.
A value calculated from data to summarize aspects of the data. For example, the mean, y-bar, and standard deviation, s, are statistics.
Define ‘Normal model’.
A useful family of models for unimodal, symmetric distributions.
Define ‘Standard Normal model’.
A Normal model, N(μ, σ), with mean μ = 0 and standard deviation σ = 1. Also called the standard Normal distribution.
Define ‘68-95-99/7 Rule’.
In a Normal model, approximately 68% of values fall within one standard deviation of the mean, approximately 95% fall within two standard deviations of the mean, and approximately 99.7% fall within three standard deviations of the mean.
Define ‘Nearly Normal Condition’.
A distribution is nearly Normal if it is unimodal and fairly symmetric. Check by looking at a histogram or a Normal probability plot.
Define ‘Normal percentile’.
The Normal percentile corresponding to a z-score gives the percentage of values in a standard Normal distribution found at the z-score or below.
Define ‘Normal probability plot’.
A display to help assess whether a distribution of data is approximately Normal. If the plot is nearly straight, the data satisfy the Nearly Normal Condition. It graphs a value according to it’s expected z-score.
How do you judge whether a value is extreme?
Use the 68-95-99.7 Rule as a rule-of-thumb.
