Math 1040 Chapter 2
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Define frequency distribution
One way to organize Qualitative Data in tables; a frequency distribution lists each category of data and the number of occurrences for each category of data.
Define relative frequency
Another way to organize Qualitative Data into a table. The relative frequency is the percentage of observations within a category and is found using the following formula:
Relative Frequency = Freq/sum of all freqs
Define relative frequency distribution
Goes hand-in-hand with relative frequency.
A relative frequency distribution lists each category of data together with the relative frequency
How is a bar graph constructed?
A bar graph is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis. Rectangles of equal width are drawn for each category. The height of each category represents the category's frequency or relative frequency.
What is a Pareto Chart?
A chart whose bars are drawn in decreasing order of frequency or relative frequency.
What is a frequency polygon?
A frequency polygon is a graph that uses points, connected by line segments, to represent the frequencies for the classes.
It is constructed by plotting a point above each class midpoint (the sum of consecutive lower class limits divided by 2) on a horizontal axis at a height equal to the frequency of the class.
We can use frequency polygons to summarize quantitative data graphically. They provide the same information as histograms.
What is cumulative frequency and relative cumulative frequency?
A cumulative frequency distribution displays the aggregate frequency of the category. In other words, it displays the total number of observations less than or equal to the upper class limit of the class.
A cumulative relative frequency distribution displays the proportion (or percentage) of observations less than or equal to the upper class limit of the class.
The cumulative frequency for the second class is the sum of the frequencies of classes 1 and 2; the cumulative frequency for the third class is the sum of the frequencies of classes1,2, and 3; and so on.
What is an "ogive"?
An ogive (read as “oh jive”) is a graph that represents the cumulative frequency or cumulative relative frequency for the class. It is constructed by plotting points whose x-coordinates are the upper class limits and whose y-coordinates are the cumulative frequencies or cumulative relative frequencies of the class. Then line segments are drawn connecting consecutive points. An additional line segment is drawn connecting the first point to the horizontal axis at a location representing the upper limit of the class that would precede the first class (if it existed).
Ogives do not have a line segment drawn from the last point to the horizontal axis because ogives represent the number or proportion of observations less than or equal to the x-coordinate of the point. Note the height of the last point in a relative frequency ogive is always 1.
Explain the difference between x-coordinates and y-coordinates for a frequency polygon and a frequency ogive:
x-coordinates for a frequency polygon are plotted above each class midpoint. x-coordinates for a frequency ogive are plotted at the upper class limits.
y-coordinates for a frequency polygon are plotted at a height equal to the frequency. y-coordinates for a frequency ogive are plotted at a height equal to the cumulative frequency or cumulative relative frequency.
What is a time-series plot?
A time-series plot is obtained by plotting the time in which a variable is measured on the horizontal axis (x-axis) and the corresponding value of the variable on the vertical axis (y-axis). Line segments are then drawn connecting the points.
Useful in identifying trends in the data over time.
Define time-series data:
If the value of a variable is measured at different points in time, then the data are referred to as time-series data.
The closing price of stock at the end of the year each year for the past 12 years is an example.
A time-series plot (does/does not) connect the graph to the x-axis. A frequency polygon (does/does not) connect the graph to the x-axis.
How does one calculate the percent change?
does not; does
to find the percent change between two values in a time-series plot:
% change = p2-p1/p1
Graphs (lead/mislead) if they (intentionally/unintentionally) create a(n) (correct/incorrect) impression.
Graphs (are supportive/deceive) if they (intentionally/unintentionally) create a(n) (correct/incorrect) impression.
mislead, unintentionally, incorrect
deceive, intentionally, incorrect
The most common graphical misrepresentations involve:
a) the scale of the graph
b) an inconsistent scale
c) a misplaced origin
d) A & B only
e) A & C only
f) all of the above
Also, because readers usually assume that the baseline is at the bottom of the graph, a graph that begins at a higher or lower value can be misleading.
Why is the use of 3D graphs strongly discouraged?
Because... (choose all that apply)
a) such graphs are often difficult to read
b) such graphs add little value to the graph
c) such graphs distract the reader from the data
a, b, and c are all reasons why 3D graphs are strongly discouraged
When comparing bars, our eyes are really comparing the areas of the bars. The bars or classes should have the same width. This ensures that the area of the bar is proportional to its height so that we can simply compare the heights of the bars. However, when we use two-dimensional pictures in place of bars, it is not possible to obtain a uniform width.
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