chapter 2 frequency tables
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Apr 3, 2024
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5. Constructing histograms and polygons
The frequency distribution table for a variable measured on a ratio scale is given here.
Score
f
5
1
4
4
3
5
2
8
1
1
Use a histogram
to graph the frequency distribution. (
Note
: You will use rectangles to construct your histogram. To plot a bar, drag a rectangle onto
the graph, position it over the score, and adjust the corners so that the bottom corners are sitting on the X-axis and the top corners have y-
coordinates equal to the score’s frequency.)
Explanation:
To construct a histogram, each of the different scores in the data set is shown on the X-axis, and a bar is plotted above each score with a height
equal to the score’s frequency (or relative frequency). No space is left between adjacent bars as a visual cue that all scores between the
smallest and largest scores are possible.
There are five different scores in this particular data set (1, 2, 3, 4, and 5), so there are five touching bars on the histogram. To plot a bar, drag
a rectangle onto the graph, position it over the score, and adjust the corners so that the bottom corners are sitting on the X-axis (have y-
Your Answer
10
8
6
4
2
0
f
SCORE
1
2
3
4
5
Correct Answer
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coordinates of 0) and the top corners have y-coordinates equal to the score’s frequency. Beginning on the left, the bars have heights of 1, 8, 5,
4, and 1.
Use a polygon
to graph the frequency distribution. (
Note
: You will use points to construct your polygon. The line segments automatically connect your
points. Lay the points of the polygon across the bottom of the graph to start; then drag each point to its correct height. This will avoid the lines
doubling back on each other.)
Explanation:
To construct a polygon, a point is plotted above each score in the data set with a y-coordinate equal to the score’s frequency (or relative
frequency). Adjacent points are connected with line segments. Two additional points are also plotted: one at the next lower score than the
lowest score and one at the next higher score than the highest score. Both points sit on the X-axis (have y-coordinates of 0). The extra points
anchor the polygon to the X-axis and provide a visual cue that there are no scores below the smallest score and no scores above the highest
score.
There are five different scores in this particular data set (1, 2, 3, 4, and 5), so there are seven points on the polygon, one for each score and
the two anchor points. To plot a score’s point, drag a point onto the graph, and position it so that its x-coordinate is equal to the score and its y-
coordinate is equal to the score’s frequency. Beginning on the left, the points have y-coordinates of 1, 8, 5, 4, and 1. Line segments will
automatically connect successive points. Then plot the two anchor points at (0, 0) and (6, 0).
Your Answer
0
1
2
3
4
5
6
10
8
6
4
2
0
f
SCORE
Correct Answer
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