Find a Median after Ordering the Data
Sort the five values and select index 2 as the middle value.
About 18 minutes, plus any extended practice
Supplied materials
- Paper and pencil; answers may also be spoken or typed.
- All cases, labels, numbers and rules are supplied on this page. No real account, private information or purchase is needed.
Learn the idea
The median is the middle value of an ordered list with an odd number of entries. Ordering is necessary, but it does not mean the original temporal order was meaningless. Here the question concerns only the median; every list contains five recorded numeric observations.
Sort the five values and select index 2 as the middle value. Do not select the third item from an unsorted original list.
Use this supplied case: Paper Python 3 expression: sorted([9,2,5,7,3])[2]. What value results? The task is to connect the given information to the computing idea. Write a short evidence trail so another learner can reproduce your choice. The simplified case describes the stated model, not every real system.
- Represent the supplied worked case with a labeled drawing, table or short trace.
- Sort the five values and select index 2 as the middle value.
- Explain why the worked answer fits and why one alternative does not.
- Try the new check and practice cases; revisit the stated rule if your evidence does not match.
See the method in action
Order [9,2,5,7,3] as [2,3,5,7,9]. Five values have a middle position at index 2, giving median 5. Order the distinct list [6,11,2,8,4] as [2,4,6,8,11]; its median is 6. Using its unsorted third entry would instead give 2. Sort before selecting the middle position; an odd count has one middle entry, while an even-count rule would need separate instruction.
Check your reasoning
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Helpful tips
- Sort the five values and select index 2 as the middle value.
- Do not select the third item from an unsorted original list.
See the answer and explanation
4
First sorting produces [1, 3, 4, 6, 8]. The sequence has positions 0→1, 1→3, 2→4, 3→6, 4→8. Select position 2, whose value is 4. Sort the five values and select index 2 as the middle value.
Take it further
New list[11, 2, 7, 4, 9]orders to[2, 4, 7, 9, 11], so median 7. Selecting the original third value happens to match here but is not a valid general method.
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More practice: try new cases
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