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There are several ways to collect and organize data.
The lesson on
measures
of central tendency shows an example of using
a tally/frequency
table. Two additional methods of organizing data are:
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frequency histograms
and
cumulative frequency histograms
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Frequency Histogram:
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| A histogram is
constructed from a frequency table, thus its name "frequency
histogram". The intervals from the table are placed
on the x-axis and the values needed for the frequencies
are represented on the y-axis. The frequencies are
depicted by the height of a rectangular bar located directly
above the corresponding interval. The
shapes of histograms may vary by changing the size of the
intervals.
Some textbooks differentiate between
histograms and bar graphs. In their definitions, a bar
graph differs from a histogram in that the rectangular bars in a
bar graph are separated from each other by a small gap. In
histograms, the bars touch each other.
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Histogram |
* Remember, if the interval
does not start at zero, leave a space before you make the first bar.
Some teachers require a symbol to be inserted to show the interval does not start at zero.
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See how to use
your
TI-83+/TI-84+ graphing calculator with
frequency histograms.
Click calculator. |
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Cumulative Frequency Histogram:
| The cumulative frequency
is the running total of the frequencies. On a
graph, it can be represented by a cumulative frequency
polygon. The graph will look like a bar graph that shows the
data after it has been added from the smallest interval to the
largest interval. |
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Frequency Histogram |
The shape of a cumulative frequency histogram will always have
the rectangular bars getting bigger as you move to the right.
Example: Start with the smallest
interval (75-79)
and add. 4 + 6
= 10;
10 + 3 = 13;
13 + 2 = 15.
15 is the total number of data
entries.
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| Math Scores |
Frequency |
Cumulative |
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75 -79 |
4 |
4 |
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80 -84 |
6 |
10 |
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85 -89 |
3 |
13 |
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90 - 95 |
2 |
15 |
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See how to use
your
TI-83+/TI-84+ graphing calculator with
cumulative frequency histograms.
Click calculator. |
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