What are the characteristics of symmetric and skewedhistograms?
See solution.
Practice makes perfect
We are asked how a symmetrichistogram is different from a skewed histogram. A histogram is a graph that represents data from a frequency table.
Example Histograms
To determine the difference between both types of histograms we will look at example graphs of each type.
Symmetric Histogram
Let's take a look at an example frequency table that represents the number of students that spend a particular number of hours per day in front of a computer.
Number of Hours
Frequency
0 - 3
2
4 - 7
7
8 - 11
12
12 - 15
8
16 - 19
1
Now we will use the intervals from the table to draw a bar for each interval. The height of each bar is equal to the frequency of its interval.
Note that the shapes on both sides of the peak of the histogram are close to mirror images. This kind of histogram is called symmetric because it has symmetry.
Skewed Histogram
Let's now look at an example frequency table representing the amount of money that a random sample of 50 customers spent in a supermarket.
Amount Spent ($)
Frequency
0-19
13
20-39
14
40-59
11
60-79
9
80-99
5
Just as we did with the previous frequency table, we will make a histogram using the data.
This histogram also has one peak, but this time the peak is not in the center. Therefore, this histogram is considered to be skewed.
Differences
Finally, we can list some of the differences that we found having analyzed both histograms.
Differences
Symmetric Histogram
Skewed Histogram
This histogram is roughly the same as its mirror image.
Higher bars are shifted to the left or right side of the histogram.
The only peak is in the center of the histogram.
The only peak is not in the center of the histogram.
