## Displaying and Summarizing Quantitative Data

Word Definition
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).
Middle 50%.
Standard Deviation Square root of variance.
Mean Average
Five Number Summary
(Smallest to Largest)
Minimum, Quartile 1, Median, Quartile 3, Maximum
"n" Sample size.
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.