Outliers in Data Sets
Understand and identify outliers in various data sets, analyze their impact, and calculate measures of central tendency with and without outliers.
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Outliers in Data Sets
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Carefully read each question and provide your answer in the space provided. Show all your work for calculations.
1. What is an outlier in a data set? Explain in your own words.
2. Consider the following data set: 12, 15, 18, 20, 22, 65. The outlier in this data set is .
3. In the data set: 5, 8, 10, 11, 13, 14, 15, 4. The number that appears to be an outlier is .
4. How does an outlier typically affect the mean of a data set?
It has no effect.
It pulls the mean towards itself.
It pushes the mean away from itself.
It only affects the median.
5. An outlier always increases the range of a data set.
True
False
6. For the data set: 10, 12, 15, 18, 20, 70
a) Calculate the mean with the outlier.
b) Calculate the mean without the outlier.
c) What do you observe about the mean when the outlier is removed?
7. Plot the data set {2, 3, 5, 6, 20} on the number line below. Circle the outlier.
8. A student's test scores are 85, 90, 88, 92, and 15. Identify the outlier and explain why it is important to consider its presence when analyzing the student's performance.