Standard Deviation
Let’s explore the impact of the outlier on the variability of the G-rated movies. In the G-rated group, select and remove the outlier of [latex]357[/latex]. As illustrated in the following screenshot, highlight the value [latex]357[/latex] and delete.
Explore the impact of removing the outlier by answering Questions 5 – 7 below. What do you notice about the variability?
question 5
question 6
question 7
video placement
[wrap-up: The goal of this activity is to understand that standard deviation is sensitive to outliers and is not a perfect measure of variability. “What did you think about how sensitive std dev is to the presence of outliers? How did the dot in the G-rated distribution affect the numerical summary? Let’s examine the range of the G-rated distribution. Note that the max value is 357, but the data is clearly concentrated between about 70 and120. Let’s look again at what happens to the mean of the distribution when we remove the outlier. The median stays about the same, which makes sense since it’s the middle data value. But the mean drops from a position well to the right of the median back to even with the median. And the variance drops from about 625 to about 121 — pretty significant! The key take-away is that our ideas of center and spread are affected greatly by the presence of outliers, and they should be used responsibly. Standard Deviation can give us an idea of variability, along with other characteristic about a distribution, but it is not a perfect measure. ]
