What you’ll learn
Analyze effects of outliers.
Key idea
Mean divides the total by the unchanged observation count.
Mean change divides total change by the fixed count; descriptive extreme does not assert an unstated outlier fence.
Worked example
Enter the exact value or ordered values in the format requested below.
Data [1, 5, 5, 9] have mean 5. Replace largest 9 by high extreme 29, keeping four observations. Find numerical new mean.
- Replacing 9 by 29 increases the total by 20, but the count stays four.
- New total 40; mean 40/4=10. The middle pair remains 5,5, so the median remains 5; no formal outlier fence is assumed.
Answer: 10
Quick Check
Evaluate a worked attempt at analyze effects of outliers, identify the first invalid step, and provide the correction.
In [4, 7, 7, 10], replace 10 by 18. Step 1 correctly finds total increase 8. Step 2 adds full increase to old mean, giving 15. Find first invalid step and correct new mean.