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Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

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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.

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.

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.

Now Katelyn is looking at humidity data. She has gathered information about the last two weeks of humidity. However, she is confused by the way the data looks on the graph. The left side of the graph almost looks symmetrical, but there is another grouping of data towards the right side of the graph. This data is **bimodal**, where the data set has two different modes. Notice below that the second peak is slightly smaller than the first peak. Therefore, this data is non-symmetric and bimodal.

Okay, take a look at this graph:

How would you describe this data based on the visual representation? Notice that the majority of the observations occur towards the right, and the tail is on the left. Therefore, we have a data distribution that is skewed left.

Visual representations are a great way of understanding data. When analyzing visual representations, you'll want to start by looking for one of two characteristics in the shape of the graph. You'll find that the graph may 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's 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.

Your graph could 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.

Once you've finished with this lesson, you should have the ability to:

- Identify the importance of visual representations of data
- Describe symmetrical and skewed graphs
- Recall how to tell whether a graph is skewed left or skewed right
- Explain what it means when data has a gap or is bimodal

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Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

- What is the Center in a Data Set? - Definition & Options 5:08
- Mean, Median & Mode: Measures of Central Tendency 6:00
- How to Calculate Mean, Median, Mode & Range 8:30
- Calculating the Mean, Median, Mode & Range: Practice Problems 7:13
- Visual Representations of a Data Set: Shape, Symmetry & Skewness 5:22
- The Mean vs the Median: Differences & Uses 6:30
- Spread in Data Sets: Definition & Example 7:51
- Maximums, Minimums & Outliers in a Data Set 4:40
- Quartiles & the Interquartile Range: Definition, Formulate & Examples 8:00
- Finding Percentiles in a Data Set: Formula & Examples 8:25
- Calculating the Standard Deviation 13:05
- The Effect of Linear Transformations on Measures of Center & Spread 6:16
- Population & Sample Variance: Definition, Formula & Examples 9:34
- Ordering & Ranking Data: Process & Example 6:54
- Go to Summarizing Data

- Go to Probability

- Go to Sampling

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