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Stat Chapter 4
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. |