Displaying and Summarizing Quantitative Data
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Distribution | Slices up all possible values of the variable into equal-width bins.
Gives counts of values falling into each bin.
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| 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.
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| Relative Frequency Histogram | Each bar represents frequency of values falling into each bin in PERCENTS.
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| Bins in Histograms | Minimum of FIVE BINS
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| Bin | Bar or class
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| Horizontal (X) Axis on Histograms | Variable.
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| Vertical (Y) Axis on Histograms | Frequency (counts or percents).
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| Stem and Leaf Display | Sketches distribution of quantitative data.
Useful for small sets of data.
MUST HAVE KEY (with units).
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| Dotplot | Graphs a dot for each case against a single axis.
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| Shape | Modes (single, multiple, etc.); Skew and Symmetry; Outliers and Gaps.
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| Modes | Unimodal (one mode); Bimodal (two modes); Multimodal (multiple modes); uniform (no modes).
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| Right Skew | Mean > Median (mean is on right).
Tail (or longest whisker) is on right.
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| Left Skew | Mean < Median (mean is on left).
Tail (or longest whisker) is on left.
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| Symmetry | Mean = Median.
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| Outlier | All outliers are influential; not all influential datum are outliers.
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| Spread | Range, IQR (Inner Quartile Range), and Standard Deviation (Variance).
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| Range | Maximum - Minimum
Not resistant to outliers.
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| Inner Quartile Range (IQR) | Q3 - Q1
More resistant to outliers (than range).
Middle 50%.
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| Standard Deviation | Square root of variance.
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| Mean | Average
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| Five Number Summary (Smallest to Largest) | Minimum, Quartile 1, Median, Quartile 3, Maximum
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| "n" | Sample size.
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| Minimum | Smallest datum in the set of data.
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| Maximum | Largest datum in the set of data.
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| Quartile 1 (Q1) | "Median of lower half".
Marks 25th percentile.
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| Quartile 3 (Q3) | "Median of upper half".
Marks 75th percentile.
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| Median (Quartile 2, Q2, or Med.) | Middle datum (but not necessarily an actual piece of data).
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| Numerical Summary (10 factors) | Mean, Standard Deviation, Range, Inner Quartile Range (IQR), "n", and Five Number Summary (Minimum, Q1, Median, Q3, and Maximum).
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| Most reliable measure of CENTER when shape is SYMMETRICAL | Mean.
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| Most reliable measure of CENTER when shape is SKEWED | Median.
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| Most reliable measure of SPREAD when shape is SYMMETRICAL | Standard Deviation.
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| Most reliable measure of SPREAD when shape is SKEWED | Inner Quartile Range (IQR).
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| Percentile | The ith percentile is the number that falls above i% of the data.
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Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
emmaherbach
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