Apply a Stated Quartile Convention

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: For sorted data [3, 5, 7, 9, 11, 13], use the median of each three-value half for Q1 and Q3. Find IQR. Candidate answers: (A) 10 (B) 2 (C) 4 (D) 6.
• Independent check inputs: For sorted data [4, 7, 10, 13, 16, 19], use the median of each three-value half for Q1 and Q3. Find IQR. Candidate answers: (A) 15 (B) 3 (C) 6 (D) 9.

Learn the idea

Data summaries describe center and spread using stated definitions. Mean, median, interquartile range and mean absolute deviation respond differently to extreme values, so the chosen measure should match the question and convention. Interquartile range subtracts the lower quartile from the upper quartile. With the stated median-of-halves convention, each quartile is the middle value of its corresponding sorted half.

Here is the method on the supplied teaching case. Q1 is the lower-half middle value 5; Q3 is the upper-half middle 11. Thus IQR=11−5=6, under the stated convention.

Quartile conventions can differ across software and sample sizes. Use the explicit convention given here; the IQR describes middle-half spread rather than the distance between the minimum and maximum.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Changed-input task: For sorted data [10, 19, 28, 37, 46, 55], use the median of each three-value half for Q1 and Q3. Find IQR. Candidate answers: (A) 18 (B) 27 (C) 45 (D) 9. Show the mathematical reason, not only the selected answer. Expected result: 27. Q1 is the lower-half middle value 19; Q3 is the upper-half middle 46. Thus IQR=46−19=27, under the stated convention.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.