What Types Of Graphs Can You Use For Quantitative Data

There are more means to summarize quantitative information than qualitative information because numerical data comes in two forms: discrete or continuous (as mentioned earlier). You lot will learn how to create tables and histograms of each type of data. 2 other summary methods for quantitative data are stem-and-leaf plots and dot-plots. These plots are rarely used except every bit preliminary (quick-and-dirty) techniques for understanding your information.

Detached Data

The methods for summarizing discrete data are similar to methods used for summarizing qualitative data, since detached data tin can be put into separate categories.

Tables

Discrete quantitative data tin can be presented in tables in several of the aforementioned ways as qualitative data: by values listed in a table, by a frequency tabular array, or by a relative frequency tabular array. The merely difference is that instead of using category names, we use the discrete values taken by the information.

Histograms

Discrete quantitative data tin be presented in bar graphs in the same means as qualitative data. A bar graph for any type of quantitative data is called a histogram. The discrete values taken by the data are labeled in ascending lodge across the horizontal axis, and a rectangle is drawn vertically then that the peak of each rectangle corresponds to each detached variable's frequency or relative frequency. The principal visual difference between a bar graph (qualitative data) and a histogram (quantitative data) is that in that location should be no horizontal spacing between numerical values forth the horizontal axis. In other words, rectangles touch each other in a histogram.

Stem-and-Leaf Plots

A stalk-and-leaf plot is a graph of quantitative data that is similar to a histogram in the style that it visually displays the distribution. A stem-and-leaf plot retains the original data. The leaves are usually the concluding digit in each data value and the stems are the remaining digits. A legend, sometimes called a cardinal, should be included and so that the reader tin can translate the information.

Constructing a Stalk‑and-Leaf Plot

Create ii columns, one on the left for stems and one on the right for leaves.
List each stem that occurs in the data ready in numerical order. Each stalk is normally listed merely once; all the same, the stems are sometimes listed two or more than times if splitting the leaves would brand the data gear up's features clearer.
Listing each leaf side by side to its stem. Each leafage will exist listed as many times as it occurs in the original data set. There should be as many leaves as there are data values. Be certain to line upwards the leaves in directly columns and then that the tabular array is visually accurate.
Create a key to guide interpretation of the stem‑and-leaf plot.
If desired, put the leaves in numerical guild to create an ordered stem-and-leaf plot .

Case i.iii: Creating a Stem-and-Foliage Plot

Create a stem-and-foliage plot of the following Human activity scores from a grouping of college freshmen.

1.3 Creating A Stem and Leaf Plot

Solution

1.3 Creating A Stem and Leaf Plot - Answer

Continuous Data

Continuous data has an infinite number of possibilities (similar weights, heights, and times). In terms of summarizing techniques, the main departure between detached data and continuous information is that continuous data cannot straight be put into frequency tables since they exercise not have any obvious categories (you lot cannot create a table or histogram with an infinite number of categories).

To get effectually this, categories are created using classes, or intervals (ranges) of numbers. Each class has a lower grade limit, which is the smallest value inside the class, and an upper grade limit, which is the largest value within the class. The class width is the deviation betwixt the upper grade limit and the lower class limit. Finally, if a class does not take a lower or upper form limit (due east.g., "shorter than 4 anxiety" or "60 and older"), the class is said to be open ended.

Tables

One time classes are established for a continuous variable, each data value will belong to one (and simply one) grade. Counts of the number of data values within each class tin now be made, resulting in a table of either a frequency distribution (raw counts) or of a relative frequency distribution (percentage).

Some expert practices for constructing tables for continuous variables are listed below. The word "reasonable" in the last 2 points is very subjective.

Classes should not overlap.
Classes should non have any gaps betwixt them.
Classes should take the same width (except for possible open up-ended classes at the farthermost low or farthermost high ends).
Class boundaries should be reasonable numbers.
A class width should exist a reasonable number.

Histograms

One time a table of values has been created for your continuous data, a histogram is created, as before, where the classes now make up the horizontal scale (call back that in a histogram, the rectangles touch on each other). One drawback with histograms of continuous data is that when changing the grade width, the appearance of the histogram can change dramatically.

A Continuous Data Instance

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The included table presents the pct of each state's residents who were living in poverty in 2002. The data includes a data value for the District of Columbia so at that place are 51 data values. I'll describe the procedure for creating frequency and relative frequency tables and their corresponding.

Frequency and Relative Frequency Tables

In simply looking over the information (which illustrates the problem of obtaining information from just a raw listing of numbers), the lowest percentage of poverty is 5.6% and the largest is xviii.0%. Since percentages are typically not discrete, we must create classes of percentages to begin summarizing the information. Permit's utilize a class width of 1 (percent) with the get-go grade limit beginning at 5%.

When labeling the class widths, you must exist careful and so that there is no overlap. If we had course widths labeled, "5 – 6," "half-dozen – vii," "vii – eight," and so on, confusion arises when you lot encounter a percentage of, say, 7.0%. Which class does the information value autumn into? "6 – seven" or "vii – 8?" Therefore, be careful and label each class every bit, "five – 5.9," "6 – 6.ix," "vii – 7.9," and then on.

Class	Frequency	Relative Frequency
v – 5.9	1	0.0196 ( = 1/51)
6 – 6.ix	ane	0.0196
seven – 7.9	3	0.0588
8 – 8.ix	7	0.1373
9 – 9.ix	9	0.1765
10 – 10.9	six	0.1177
11 – 11.9	5	0.0980
12 – 12.nine	3	0.0588
13 – 13.ix	5	0.0980
14 – xiv.9	iv	0.0784
15 – xv.9	1	0.0196
sixteen – 16.9	2	0.0392
17 – 17.9	iii	0.0589
18 – 18.nine	1	0.0196

How you round the percentages in the "Relative Frequency" cavalcade is a matter of taste. Just make certain not to round as well much or to carry unnecessary decimals.

Histograms of the Frequency and Relative Frequency Table Results

I'm using Excel for this, although if you're conscientious, you can draw them by hand.

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Observe that, as with bar graphs, both histograms have exactly the same shape. The just departure is the vertical calibration. Information technology's up to yous, and the betoken you're trying to become beyond to your audition, which graphical summary to present.

If we repeat the above process with a class width of two, rather than 1, we get the post-obit table and histograms:

Class	Frequency	Relative Frequency
5 – half-dozen.9	2	0.0392 ( = 2/51)
seven – eight.9	10	0.1961
9 – 10.9	xv	0.2941
eleven – 12.9	8	0.1569
13 – 14.9	9	0.1765
15 – 16.9	iii	0.0588
17 – 18.ix	iv	0.0784

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Notice the differences between the histograms for class widths of 1% and 2%. Which histogram better conveys the information from the data? Why? Detail can be lost when grouping too much data together. On the other mitt, if too many classes have no data values (counts of 0 or one), so the histogram is probable likewise specific. You may have to experiment with a few histograms and cull the one that looks best. Again, this can be a thing of sense of taste.

Describing the Shape of a Histogram

Ane important characteristic of continuous data is that we can describe its distribution. This results from continuous data having a unique ordering of possible values (since information technology is numerical). In plain terms, a distribution shows how data values are spread out (or distributed) across all possible results. We will focus mainly on i specific distribution in class, the Normal distribution, but you should keep in listen that this is only one of possibly infinite distributions of data. Wikipedia has an impressive list of many of the more of import detached and continuous distributions that often arise in statistical studies. See:

http://en.wikipedia.org/wiki/List_of_probability_distributions

In that location is a set of common linguistic communication to describe the overall shape of data distributions. Are all the rectangles (roughly) the same peak for each category? Is in that location ane fundamental peak, with frequencies failing off in either direction? Here are the common shapes nosotros'll encounter:

Uniform Distribution: A distribution where each of the values tends to occur with the same frequency. In this case, the histogram looks flat.

Bell-Shaped Distribution: A distribution where most of the values fall in the centre (a central elevation), and the frequencies tail off to the left and to the correct. A bong-shaped distribution is called symmetric, where both the right and left sides have (roughly) the same shape.

Correct-Skewed Distribution: A distribution that is not symmetric, and where the tail to the right is longer than the tail to the left.

Left-Skewed Distribution: A distribution that is not symmetric, and where the tail to the left is longer than the tail to the right.

If y'all wait to the histograms of class width 1% created for the previous case, information technology is clear that these are right-skewed distributions, since the summit of values tends to fall effectually nine%, and there is a tail of values extending far to the correct, all the fashion out to xviii%.

Time-Series Data

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When a variable of interest is measured at different points in time, the information is time-serial data. This ways that time is the variable on the horizontal axis. Such a plot is called a time-series plot. Time series plots are used to identify long-term trends in a variable, or to place regularly occurring trends. This time-series plot illustrates how fetal head circumference changes throughout a gestational flow. Observe the roughly linear pattern. This information can be used to place changes in or problems with fetal growth.

Careful Graphical Techniques

Statistical displays can distort the truth. Information technology's frightening how easy information technology can exist to mislead or even deceive people with graphical summaries. If you unintentionally distort the truth with a bad graph, this is called misleading. If you intentionally misconstrue your results, this is chosen deceiving. Many people, including scientists and peculiarly the media, are guilty of both.

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If you want to illustrate a certain point, but your graphical summary does non support your point, it is relatively simple to make changes (for example, to rectangle heights or vertical/horizontal scales) that will then lend credibility to your indicate. For example, wait at the two graphs provided hither, which illustrate the average distance of PGA golfers' drives off the tee for the ten-year period 1997 – 2006. The graph on the left shows a sharp increment in driving distance over the years, while the graph on the right shows little, if no, increase in driving distance at all. Both are from the aforementioned gear up of information! The difference between the 2 graphs is the pick of vertical scale. While the graph on the left shows distances from 250 – 300 yards, the graph on the correct shows distances from 0 – 400 yards. In other words, the graph on the left has zoomed in on the relevant range of distances.

Although no social or political impairment can come from misleading the public on golf driving distances, there are many issues where certain groups can easily deceive the public by showing graphs in ways that illustrate the point(s) they are trying to get across. It is up to you to have a few moments when you see a graphical summary of someone'south information to see what is actually going on.

Summary

Qualitative Data

Summary of Qualitative Data - Visual