|Distribution||Slices up all possible values of the variable into equal-width bins.
Gives counts of values falling into each bin.
|Histogram||Show distribution of a quantitative variable.
Each bar represents frequency (counts) of values falling into each bin.
Bars can touch.
MUST HAVE FREQUENCY TABLE.
|Relative Frequency Histogram||Each bar represents frequency of values falling into each bin in PERCENTS.|
|Bins in Histograms||Minimum of FIVE BINS|
|Bin||Bar or class|
|Horizontal (X) Axis on Histograms||Variable.|
|Vertical (Y) Axis on Histograms||Frequency (counts or percents).|
|Stem and Leaf Display||Sketches distribution of quantitative data.
Useful for small sets of data.
MUST HAVE KEY (with units).
|Dotplot||Graphs a dot for each case against a single axis.|
|Shape||Modes (single, multiple, etc.); Skew and Symmetry; Outliers and Gaps.|
|Modes||Unimodal (one mode); Bimodal (two modes); Multimodal (multiple modes); uniform (no modes).|
|Right Skew||Mean > Median (mean is on right).
Tail (or longest whisker) is on right.
|Left Skew||Mean < Median (mean is on left).
Tail (or longest whisker) is on left.
|Symmetry||Mean = Median.|
|Outlier||All outliers are influential; not all influential datum are outliers.|
|Spread||Range, IQR (Inner Quartile Range), and Standard Deviation (Variance).|
|Range||Maximum – Minimum
Not resistant to outliers.
|Inner Quartile Range (IQR)||Q3 – Q1
More resistant to outliers (than range).
|Standard Deviation||Square root of variance.|
|Five Number Summary
(Smallest to Largest)
|Minimum, Quartile 1, Median, Quartile 3, Maximum|
|Minimum||Smallest datum in the set of data.|
|Maximum||Largest datum in the set of data.|
|Quartile 1 (Q1)||"Median of lower half".
Marks 25th percentile.
|Quartile 3 (Q3)||"Median of upper half".
Marks 75th percentile.
|Median (Quartile 2, Q2, or Med.)||Middle datum (but not necessarily an actual piece of data).|
|Numerical Summary (10 factors)||Mean, Standard Deviation, Range, Inner Quartile Range (IQR), "n", and Five Number Summary (Minimum, Q1, Median, Q3, and Maximum).|
|Most reliable measure of CENTER when shape is SYMMETRICAL||Mean.|
|Most reliable measure of CENTER when shape is SKEWED||Median.|
|Most reliable measure of SPREAD when shape is SYMMETRICAL||Standard Deviation.|
|Most reliable measure of SPREAD when shape is SKEWED||Inner Quartile Range (IQR).|
|Percentile||The ith percentile is the number that falls above i% of the data.|