• Data can be symmetric or skewed left or right
• Skewed left implies the mean is less than the median and there is a larger ‘spread’ of the data on the left side
• Skewed right implies the mean is greater than the median and there is a larger ‘spread’ of the data on the right side
• See the detailed explanations and videos in the sections below.

Symmetric Distributions

The mean and median are roughly equal The histogram should have equal length ‘tails’ above and below the median/mean If the shape of the histogram is the ‘bell-shaped‘ we can infer that it follows a Normal Distribution (more on this distribution type to come in later sections)
The boxplot should have roughly equal length halves of the box above/below the median There should be roughly the same length of the whiskers above/below the median If there are outliers, they should be roughly the same distance above/below the median

SKewed Right Distributions

The mean is greater than the median The histogram should have longer ‘tail’ on the right Ie: there are more extreme upper values than lower values in the data
The upper half of the box should be longer than the lower half The whisker might be longer on the upper end (above Q3) If there are outliers, there should be more outliers on the upper end (above Q3)

Skewed Left Distributions

The mean is less than the median The histogram should have longer ‘tail’ on the left Ie: there are more extreme lower values than upper values in the data
The lower half of the box should be longer than the upper half The whisker might be longer on the lower end (below Q1) than the upper end (above Q3) If there are outliers, there should be more outliers on the lower end (below Q1)

Analyzing Skewness in Excel Graphs (video)

Example 13.1.1

Problem Setup: Again, we are working with the student survey data (click here to download).

Question: How can we tell from the boxplot and histogram that the students’ heights are skewed left? .. Watch the video below to find out!

Solution: Click here to view the Excel solutions shown in the above video.

Key Takeaways (EXERCISE)

Your Own Notes (EXERCISE)

• Are there any notes you want to take from this section? Is there anything you’d like to copy and paste below?
• These notes are for you only (they will not be stored anywhere)
• Make sure to download them at the end to use as a reference