Chapter 2: Displaying Quantitative Data
All graphs should have the following:
1. A clear title.
2. Properly labeled and scaled axes.
3. Clear unbroken lines. (Truncating is the process of trimming off the unused piece of the axis. This is designated by
4. A strict adherence to the area principle- the area occupied by a part of the graph should correspond to the magnitude of the value it represents.
Graphs for quantitative data
1. histogram-Looks almost like a bar graph except the bars touch whereas they don’t in a bar graph.
Steps:
I. Divide the range into classes of equal width.
II. Count the number of observations in each class (frequency) or the
percentage of observations in each class (called the relative frequency).
III. Draw the histogram with the y-axis as the frequency and the x-axis as
the classes.
Things to remember:
I. Each observation should fall into only one class.
II. The left interval of each class is typically “greater than.” The right
interval of each class is typically “less than or equal to.”
III. Too few classes will make your histogram look like a skyscraper and
too many will make it look like a pancake.
IV. In a histogram the x-axis has scale whereas in a bar graph the x-axis
has no scale (it just identifies the items being compared).
V. If there is a gap in the columns of the histogram, then that class has
zero objects in it.
2. Stemplot- is another method for displaying quantitative data except that this display will preserve the values whereas a histogram will not.
Steps
1. Separate each data point into a leaf (the final digit) and the stem (the
rest of the number)
2. Write the stems in a vertical column with the smallest at the top and
draw a vertical line to the right of them.
3. Write each leaf in the row to the right of its stem, in increasing order out
from the stem.
Note:
1. You can also split the stems. This method involves 1) doubling each stem, 2) putting leaves 0-4 on the upper stem, and 3) putting leaves 5 to 9 on the lower stem.
2. You can also display two comparable distributions using a back-to-back stem plot. This method involves placing the leaves of one distribution in the left column and one in the right column.
3. Dotplot- is another method for displaying quantitative data that preserves the values of the data.
I. Draw a number line and place each possible value of the variable on it. Then
place dots above the value for each case of the data.
II. This works for a small set of quantitative data over a small range of values.
Examining distributions
1. Look at the overall pattern.
a. shape-
Is it skewed to the left? The longer tail is on the left.
Is it skewed to the right? The longer tail is on the right.
Is it symmetric?
Is it uniform?
b. center- Where is the midpoint?
The mode is the central hump in the graph. Histograms with two peaks are called bimodal. Histograms with three or more peaks are called multimodal. Uniform distributions have no modes.
c. spread
2. Also look for any deviations from the pattern.
a. An outlier is any individual value that falls outside the pattern.
b. These outliers must be heavily scrutinized. They may be deleted or corrected, if a mistake has been made. Or, they may be left untouched, if no mistake in the data can be found.
Another type of graph is a time plot. If the data is measured over some time interval then you should use this type of graph.
Steps
1. Draw the x-axis as the time and the y-axis as your data.
2. Connect the data points to help emphasize any changes over time.
When describing the distribution talk about any trend (does the value of the variable increase or decrease over time?) and any cycle (does there appear to be a pattern of increases and decreases over time?).
What can go wrong?
1. Making a histogram for qualitative data.
2. Using an inappropriate scale. Your histogram will “pancake” or “skyscraper”.
3. Using inconsistent scales.
4. Not clearly labeling.