Standardizing
done to eliminate units; values can be compared and combined even if the original variables had different units and magnitudes
Standardized value
value found by subtracting the mean and dividing by the standard deviation
Shifting
Adding constant to each data value adds same constant to mean, median, and quartiles, but doesn't change standard deviation or IQR
Rescaling
multiplying each data value by a constant multiplies both the measures of position and the measures of spread by that constant
Normal Mode
useful family of models for unimodal, symmetric distributions
Parameter
Numerically valued attribute of a model ; i.e., values of mu (?) and sigma (?) in a N(?,?) model
Statistic
Value calculated from data to summarize aspects of the data, (i.e., the mean, y, and standard deviation, s, are these)
z-score
Tells how many standard deviations a value is from the mean; have a mean of zero and a standard deviation of one
Standard Normal Model (Standard Normal Distribution)
a normal model, N(?,?) with mean=0 and standard deviation=1
Nearly Normal Condition
A distribution is nearly normal if it is unimodal and symmetric. We can check by looking at a histogram or a normal probability plot
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 deviations of the mean
Normal Percentile
When corresponding to the z-score, it gives the percentage of values in an SD distribution found at that z-score or below
Normal Probability Plot
a display to help assess whether a distribution of data is approximately normal; if it is nearly straight, the data satisfy the nearly normal condition