Outliers, Missing Pieces, and Wrong Numbers! (Statistics)

Introduction

Imagine you're trying to figure out the average height of your classmates. You measure everyone and write down their heights. But what if one student is much taller than everyone else, like a star basketball player? Or what if some students are absent and you can't measure them? These situations can affect how accurate your average height is.

In statistics, we deal with data all the time. Just like in our height example, the quality of that data can affect our results. Today, we'll explore three things that can mess with our data:

1. Extreme Data Points (Outliers): These are data points that fall way outside the normal range. Like the super tall student in our height example.
2. Missing Values: Sometimes, data might be missing entirely. Maybe someone forgot to record a height, or a survey question was left blank.
3. Incorrect Values: Data can also be simply wrong. Maybe a measurement was misread, or someone accidentally entered the wrong information.

So, how do these issues affect our calculations?

• Outliers: A single outlier can pull the average way off. If the average height in our class was 5'5" and the basketball player was 6'8", the average would jump way up, not reflecting most students' heights.
• Missing Values: The fewer data points we have, the less accurate our calculations become. Imagine trying to find the average with only half the class measured!
• Incorrect Values: Wrong data throws everything off! It's like using the wrong ingredients in a recipe – the results won't be what you expected.

What can we do?

• Spotting Outliers: We can use tools like boxplots to identify outliers. These plots show the spread of the data, and outliers will appear as points far from the main group.
• Dealing with Missing Values: Sometimes, we can estimate missing values based on other data. For example, if we know the average height for boys and girls in our school, we might estimate a missing height based on the student's gender. But it's important to acknowledge that this is an estimate, not a real data point.
• Checking for Incorrect Values: Double-checking data entry and looking for inconsistencies can help catch errors.

Remember: Data quality is key to getting reliable results. By being aware of outliers, missing values, and incorrect data, we can make sure our calculations are as accurate as possible!

Now it's your turn!

1. Think of an example from your own life where data quality might be an issue.
2. How could outliers, missing values, or incorrect data affect the results?
3. What could you do to improve the data quality?

Independent Practice

Now complete the independent practice sheet (located in resources section).

Use the student worksheet (under the resources tab) to assess student understanding.