Standard Deviation & Normal Model Flashcards
Standardize (what & why)
A procedure to eliminate units so that 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 …changes these values but not these other values.
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 …also changes these 5 values
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 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.
Statistic
A value calculated from data to summarize aspects of data. For example, mean and standard deviation.
z-score
This number tells how many standard deviations a value is from the mean; they have a mean of 0 and a standard deviation of 1.
Standard Normal model (or distribution) notation
N(μ,σ) with mean μ=0 and standard deviation σ=1.
Nearly Normal Condition
When the distribution is unimodal and symmetric. Check by looking at a histogram or a Normal probability plot.
68-95-99.7 Rule
In a Normal model, these percentages of values fall within 1, 2, and 3 (respectively) standard deviations of the mean.
Normal percentile
The percentile of values in a standard Normal distribution that fall below the corresponding z-score.
Normal probability plot
If the points in this type of plot are nearly straight, then the distribution of data meets the Nearly Normal Condition.
