Chapter 5

Standardize

We ___________ to eliminate units. ____________ values can be compared and combined even if the original variables had different units and magnitudes.

Standardized value

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

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.

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.

Normal (or Gaussian) model

A useful family of models for unimodal, symmetric distributions.

Parameter

A numerically valued attribute of a model. For example, the values of μ and σ in a N(μ, σ) model are _________.

Statistic

A value calculated from data to summarize aspects of the data. For example, the mean, y, and standard deviation, s, are __________.

68-95-99.7 Rule

In a Normal model, about __% of values fall within 1 standard deviation of the mean, about __% fall within 2 standard deviations of the mean, and about ____% fall within 3 standard deviations of the mean.

Standard Normal model (or Standard Normal Distribution)

A ________ ______ _____, N(μ, σ) with mean μ = 0 and standard deviation σ = 1.

Nearly Normal Condition

A distribution is in ______ ______ _________ if it is unimodal and symmetric. We can check by looking at a histogram or a Normal probability plot.

Sampling distribution

The ________ ____________ of a statistic is the distribution of all values of the statistic if it was computed for every possible sample (of a given size). We can approximate it by drawing many samples and making a histogram of the resulting statistic values.

Normal percentile

The ______ __________ corresponding to a z-score gives 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.

z-score

A _______ tells how many standard deviations a value is from the mean; ________ have a mean of 0 and a standard deviation of 1.