Outlier Detection Statistics Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumTest scores: 72, 75, 78, 80, 82, 85, 88, 90, 92, 95. A new student's score of 25 is added. How does this outlier affect the mean and median?
Solution
- 1 Step 1: Original mean: . Original median: .
- 2 Step 2: New mean: . New sorted data: 25,72,...,95. New median: 6th value = 82.
- 3 Step 3: The mean dropped by 5.3 points (from 83.7 to 78.4) while the median dropped by only 1.5 points (from 83.5 to 82). The mean is much more sensitive to outliers.
Answer
Mean dropped from 83.7 to 78.4 (−5.3 points). Median dropped from 83.5 to 82 (−1.5 points). The mean is more affected by the outlier.
Outliers disproportionately affect the mean because the mean uses every value in its calculation. The median, which depends only on the middle position, is resistant to outliers. This is why the median is often preferred for skewed distributions or data with outliers.
About Outlier Detection
Outlier detection is the process of identifying data points that are unusually far from the rest of the dataset, using techniques like the IQR rule, z-scores, or visual inspection of box plots and scatter plots. These anomalous values may indicate measurement errors, data entry mistakes, or genuinely extreme observations.
Learn more about Outlier Detection →More Outlier Detection Examples
Example 1 easy
The data set is: 10, 12, 11, 13, 12, 14, 11, 50. Identify the outlier and explain how you know.
Example 3 mediumA scientist records reaction times (ms): 245, 260, 255, 270, 250, 980, 265, 258. Use the [formula] r
Example 4 hardA data set has mean [formula] and standard deviation [formula]. Using the z-score method, determine