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.
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.
We standardize to eliminate units. Standardized values can be compared and combined even if the original variables had different units and magnitudes.
A value found by subtracting the mean and dividing by the standard deviation.
A useful family of models for unimodal, symmetric distributions.
A numerically value attribute of a model. For example, the values of mean and standard deviation in a Normal Model are parameters.
A value calculated from data to summarize aspects of the data. For example, the mean and standard deviation are statistics.
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
A Normal Model with mean = 0 and standard deviation = 1.
68% fall within 1 SD from the mean, 95% fall within 2 SD's from the mean, 99.7% fall within 3 SD's from the mean.
Corresponds to the z-score giving the percentage of values in a standard Normal 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 the plot is nearly straight, the data satisfy the Nearly Normal Condition.
Changing center & spread
Equivalent to changing its units.