Visual Representations of a Data Set: Shape, Symmetry & Skewness

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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Visual representations are a fantastic way of understanding and analyzing your data. Use this lesson to understand the characteristics of visual representations of data.

Visual Representations of a Data Set

Katelyn is a meteorologist at a local television station. She has been monitoring the data on the high temperatures of the past two weeks. Katelyn wants to use graphical representations of this data to show her viewers what's happening with the weather. She can do this by using visual representations of the data and discussing the shape, symmetry and skewness of the data. Let's take a look at the data set for Katelyn's viewers. I've arranged this data in ascending order: 72, 74, 74, 75, 75, 76, 76, 76, 77, 77, 78, 78, 79.

Now let's look at some visual representations of this data, but before we do that, we need to define a few key terms. When looking at a visual representation of a data set, you need to look for two different things: symmetry and skewness. Sometimes the representation will be symmetrical, where the shape created is mirrored nearly perfectly across a line. In statistics, you'll find that visual representations of data will be nearly perfect, but not always perfect. That is why we define symmetry as being nearly perfect. When a data set is symmetrical, then the mean, median and mode all occur in the same point. This is considered normal distribution; we won't go into normal distribution in this lesson, but check out our other lessons to learn more. It is important to keep data symmetry in mind when working with distributions.

Okay, if your visual representation of a data set is not symmetrical, then it might be skewed, which is where the shape of a graph peaks to the left or the right of the center. If a visual representation shows skewness, then the data is not normally distributed and is considered either skewed left or skewed right. Distributions that are skewed to the right have fewer observations, or numbers, that are higher values, while distributions that are skewed to the left have fewer observations, or numbers, that are lower values. You can remember this by looking at the tail of the data. If the tail is on the left side of the graph, then the distribution is skewed left. If the tail is on the right side of the graph, then the distribution is skewed right.

Analyzing Visual Representations of Data

This is a graph of the high temperatures Katelyn observed during the past two weeks:

The horizontal axis represents the temperature, while the vertical axis represents the number of days that temperature was observed. Notice that there is a central peak on this graph with each side of the peak mirroring the other. This is a symmetrical data distribution. The mean, median and mode of this data set are 76.

This is a graph of the low temperatures Katelyn observed during the past month:

Notice that the majority of the observations are concentrated to the left side of the graph. Also, notice that there aren't any days that had a low temperature of 62 degrees. This is called a gap in the data. A gap is an area in the data set where no observations have been made. Therefore, this data is skewed right and has a gap in the distribution.

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