Graphs are a good way to display and analyze data. The graph at the right is a line graph. It shows trends or changes over time. There are no holes in the graph and every point on the graph has meaning.
To construct a line graph, include the following items.
1.
a
title
2.
a
label on each axis describing the variable that it represents
3.
equal
intervals on each axis
Note that the graph at the right contains all three items.
Example
Travel Link
1. The number of annual visitors to the Grand Canyon is
given in the table at the right. Construct a line graph of the data. Then use
the graph to predict the number of annual visitors to the Grand Canyon in the
year 2010.
Alternative Solutions :
Step 1 Draw a horizontal axis and a vertical
axis and label
them as shown below. Include a title.
Step
2 Plot the points.
Step
3 Draw a line by connecting the points.
You
can see from the graph that the general trend is that the number of visitors to
the Grand Canyon increases steadily every ten years. A good prediction for the year
2010 might be about 6 or 6.5 million people.
Another
type of graph that is used to display data is a histogram. A
histogram uses data from a frequency table and displays it over equal
intervals. To make a histogram, include the same three items as the line
graph: title, axes labels, and equal intervals. In a histogram, all bars
should be the same width with no space between them.
Example
Physical Science Link
2. The
frequency table is from Example 2 in Lesson 1–6. It shows the various time
intervals that “charged” balloons remained stuck to the wall. Construct a histogram
of the data.
Alternative Solutions :
Step 1
Draw a horizontal axis and a vertical
axis and label them as
shown below. Include the title.
Step 2
Label equal intervals given in the
frequency table on the
horizontal axis. Label equal intervals of 1 on the vertical
axis.
Step 3
For each time interval, draw a bar
whose height is given by
the frequency.
Example
3. The
ages of people who participated in a recent survey are shown in the table at
the right. Construct a cumulative frequency histogram to display the data.
Alternative Solutions :
First, make
a cumulative frequency table. Then construct a histogram using the cumulative
frequencies for the bar heights. Remember to label the axes and include the
title.
Another way to display data is a stem-and-leaf plot.
In the stem-and-leaf plot at the
right, the data are represented by three-digit numbers. In this case, use the
digits in the first two place values to form the stems. For example, the values
for 102, 108, 114, 115, 125, 127, 131, and 139 are shown in the stem-and-leaf
plot at the right.
Example
School Link
4. The table
shows the class results on a 50-question test. Make a stem-and-leaf plot of the
grades.
Alternative Solutions :
The tens digits are the stems, so the stems are 1,
2, 3, and 4. The ones digits are the leaves.
Now arrange the leaves in numerical order to make the results easier to observe
and analyze.
What
were the highest and lowest scores?
49 and 13
Which
score occurred most frequently?
29 and 37, three times each
How
many students received a score of 35 or better?
11 students
Sumber
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