How an Outlier Changes the Mean and Median: A Five-Number Example

A single extreme observation can move the mean sharply while leaving the median unchanged. The median depends on ordered position; the mean uses every value.

Start with two different questions

The mean answers a total-sharing question: if the sum were distributed evenly, how much would each observation receive? The median answers a position question: what is the middle value after sorting? Neither question is automatically better. Choose the measure that matches the description you need, and report enough context to avoid hiding important variation.

Here, an outlier means a value noticeably separated from the rest for illustration. We are not applying a formal statistical rule to label observations. An unusual value may be real and important. Never delete a value merely because it makes an average less convenient.

Worked comparison

Consider five completion times, in minutes: 8, 9, 10, 11, 12. Their total is 50, their mean is 10, and their median is the third sorted value, also 10. Now replace the final time, 12, by 52. The ordered list becomes 8, 9, 10, 11, 52. The new total is 90, so the mean is 18. The median is still 10.

The mean rose by 8 because the total rose by 40 and the count stayed 5: 40/5 = 8. The centre position did not move, so the middle entry stayed the same. A reader told only “average time 18 minutes” might imagine that most times were near 18, even though four of the five times are between 8 and 11.

When can the median change?

The median is resistant to extremes, not immune to changes. Replacing the central observation or moving a value across the central position can change it. With an even number of entries, the median averages two middle values. Sorting is essential: the third number written in an unsorted list need not be the median.

A useful comparison is to report both mean and median, the sample size, and a simple spread measure. If these are classroom marks, also consider whether different tests have different totals. Combining marks expressed on incompatible scales can create a misleading result before outliers are even considered.

Common mistake

Do not conclude that an unchanged median means the entire data set is unchanged. The highest value and the spread changed greatly in this example. Conversely, a shifted mean does not prove that every observation improved or worsened. An average compresses information; it does not describe all individual entries.

Ek bahut bada number mean ko kheench sakta hai; median ke liye pehle order dekho.

Try three questions, then check the working

1. Find mean and median of 3, 4, 5, 6, 22.

   The sum is 40, so the mean is 40/5 = 8. The list is sorted, and its third value is 5, so the median is 5.

2. Change 22 to 42 in the previous list. What changes?

   The total increases by 20, so the mean increases by 20/5 = 4 to 12. The median remains 5 because the middle position is unchanged.

3. Find the median of 2, 3, 7, 8, 30, 40.

   There are six observations. Average the third and fourth sorted entries: (7 + 8)/2 = 7.5. Do not choose only one middle value.

Build the next step

• Mean from a Frequency Table
• Statistics Class 10 Notes: Mean, Median, Mode Formulas and Solved Examples

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Reference and authorship

The examples and practice questions here are original, with calculations checked separately. Definitions and related background: OpenStax: Measures of the Center of the Data. Prepared with AI assistance and editorial arithmetic review; no textbook affiliation is claimed.