5. BIVARIATE
FREQUENCY
"Bivariate" means you will have two variables. Each question in a survey
would be considered a variable, so a bivariate analysis could involve two
questions from a survey. "Frequency" means you will be counting
something, for instance the number of people who give a specific answer
to a particular question. For a bivariate frequency distribution you could
count the number who gave a specific answer to one question and a
specific question to a second question.
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6. HISTOGRAM
In statistics, a histogram is a graphical display of tabulated frequencies,
shown as bars. It shows what proportion of cases fall into each of several
categories. A histogram differs from a bar chart in that it is the area of the bar
that denotes the value, not the height, a crucial distinction when the
categories are not of uniform width (Lancaster, 1974). The categories are
usually specified as non-overlapping intervals of some variable. The
categories (bars) must be adjacent.
The word histogram is derived from Greek: histos anything set upright' (as
the masts of a ship, the bar of a loom, or the vertical bars of a histogram);
gramma 'drawing, record, and writing’. The histogram is one of the seven
basic tools of quality control, which also include the Pareto chart, check
sheet, control chart, cause-and-effect diagram, flowchart, and scatter
diagram. A generalization of the histogram is kernel smoothing techniques.
This will construct a very smooth probability density function from the
supplied data.
An example histogram of the heights of 31 Black Cherry trees.
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7. FREQUENCY POLYGONS
Frequency polygons are a graphical device for understanding the shapes of
distributions. They serve the same purpose as histograms, but are especially
helpful in comparing sets of data. Frequency polygons are also a good
choice for displaying cumulative frequency distributions.
To create a frequency polygon, start just as for histograms, by choosing a
class interval. Then draw an X-axis representing the values of the scores in
your data. Mark the middle of each class interval with a tick mark, and label
it with the middle value represented by the class. Draw the Y-axis to
indicate the frequency of each class. Place a point in the middle of each class
interval at the height corresponding to its frequency. Finally, connect the
points. You should include one class interval below the lowest value in your
data and one above the highest value. The graph will then touch the X-axis
on both sides.
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8. PIE CHART
The following few paragraphs tell you a bit about Pie Charts. A pie chart (or
a circle graph) is a circular chart divided into sectors, illustrating relative
magnitudes or frequencies or percents. In a pie chart, the arc length of each
sector (and consequently its central angle and area), is proportional to the
quantity it represents. Together, the sectors create a full disk. It is named for
its resemblance to a pie which has been sliced.
While the pie chart is perhaps the most ubiquitous statistical chart in the
business world and the mass media, it is rarely used in scientific or technical
publications. It is one of the most widely criticized charts, and many
statisticians recommend to avoid its use altogether, pointing out in
particular that it is difficult to compare different sections of a given pie
chart, or to compare data across different pie charts. Pie charts can be an
effective way of displaying information in some cases, in particular if the
intent is to compare the size of a slice with the whole pie, rather than
comparing the slices among them. Pie charts work particularly well when
the slices represent 25 or 50% of the data, but in general, other plots such as
the bar chart or the dot plot, or non-graphical methods such as tables, may
be more adapted for representing information. The earliest known pie chart
is generally credited to William Playfair's Statistical Breviary of 1801.
Pie chart of populations of English native
speakers
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