A changed extreme value can affect summaries differently
The arithmetic mean is the sum divided by the number of observations. The median is found from the ordered data: the middle value for an odd count, or the average of the two middle values for an even count. These operations summarise different aspects of a record. A data question may ask for either, so choose the specified operation before deciding which answer looks typical. Original worked records:2, 3, 3, 4, 28. Their sum is 40, so their mean is 8; their median is the third ordered value, 3. Suppose a documented audit establishes that 28 should be 8. The new sum is 20 and mean is 4, while the ordered middle value stays 3. A correction can therefore change the mean without changing the median. The calculation is not an instruction to delete an inconvenient observation: the audit supplies a reason to replace this particular entry. For six ordered values 2, 3, 3, 4, 8, 10, the two middle positions are third and fourth. The median is(3+4)/2=3.5, even though 3.5 is not itself an observed value. This is another reason to use ordered position rather than choose the largest, most frequent or most recently corrected entry. Always state the unit inherited from the original measurement; a summary of lengths remains a length. OpenStax explains why a median is less sensitive than a mean to the precise size of an extreme value. That does not make one measure universally best or establish that an extreme value is erroneous. In this pilot, the learning target is choosing and explaining the requested summary, checking arithmetic and retaining the record’s provenance. ATI also assesses wider statistical information and variable relationships that this short unit does not fully cover.
An original five-record set is 4, 4, 5, 5, 70. An audit establishes that the last value should be 7 rather than 70. What happens to the mean and median when this correction is made?
- Before correction the mean is 88/5=17.6; afterward it is 25/5=5. Both ordered lists have 5 as their third value, so the median remains 5. The audit, not a wish to remove an outlier, establishes the replacement.
Compare the other answer choices
The sum falls by 63, so its five-value arithmetic mean cannot remain unchanged.
The median uses ordered position, not every value’s numerical size.
The corrected entry remains the largest, not the middle of this five-value set.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which evidence or rule supports your decision and why the alternatives do not fit.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
OpenStax Introductory Statistics 2 e §2.5 Measures of the CenterATI TEAS Version 7 Content Outline