Final answer:
An outlier can significantly alter the five number summary by affecting the minimum or maximum, the interquartile range, or even the median. It is important to examine outliers carefully to determine if they should be included in the analysis as they can represent valuable or erroneous data.
Step-by-step explanation:
Effects of an Outlier on the Five Number Summary
The presence of an outlier can significantly impact the five number summary in statistics, which includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. An outlier can alter the range by becoming the new maximum or minimum and can affect the interquartile range (IQR) if it is located near Q1 or Q3. Additionally, if the outlier is extreme enough, it can also skew the median, especially in smaller datasets. When outliers are present, the data may appear more spread out, and the box plot may show longer whiskers or more asymmetry. Analyzing outliers is crucial since they can indicate data entry errors, or they may represent a true variation in the data that is important for a certain study.
Outliers also affect the calculation of the standard deviation and can influence the results of regression analysis, including the slope of the best-fit line and the correlation coefficient, r. If the exclusion of an outlier does not significantly change these, it may not be deemed an influential point, but if it does, the data must be reevaluated. The examination of outliers should account for the context, and it's best to determine if they are indicative of a true phenomenon or a mistake before deciding to exclude them from the data set.