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Median of a Data Set

A public descriptive-statistics question that shows how to find the median of an even-sized data set and how it differs from the mean.

Question

A courier records the number of packages delivered on six days: 9,12,14,20,25,289, 12, 14, 20, 25, 28. What is the median number of packages?

  1. a.1414
  2. b.1717
  3. c.1818
  4. d.2020

Correct answer

B. 1717

Full reasoning

  1. 1The values are already ordered: 9,12,14,20,25,289, 12, 14, 20, 25, 28, and there are 66 of them.
  2. 2With an even count, the median is the mean of the two middle values, here the third and fourth: 1414 and 2020.
  3. 3Average them: (14+20)÷2=34÷2=17(14 + 20) \div 2 = 34 \div 2 = 17, which differs from the mean of 1818.

Why each choice is right or wrong

Choice A

This picks only the lower of the two middle values instead of averaging the third and fourth values of the ordered list.

Choice B

Correct. With six ordered values the median averages the third and fourth: (14+20)÷2=17(14 + 20) \div 2 = 17.

Choice C

This is the mean, 108÷6=18108 \div 6 = 18, which answers a different measure of center than the median.

Choice D

This picks only the upper of the two middle values instead of averaging the third and fourth values of the ordered list.

Related formula

Median of an even-sized data set

median=x(n/2)+x(n/2+1)2\text{median} = \frac{x_{(n/2)} + x_{(n/2 + 1)}}{2}

Assumptions: The data are sorted in increasing order before the middle positions are read off.

Related topic and practice

Descriptive StatisticsProbability and CountingAddition Rule of ProbabilityCombinationsTwo draws without replacementZ-Scores on a Normal DistributionCreate a free account to practice

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Sources

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. Introductory Statistics 2e, Section 2.5: Measures of the Center of the Data — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.
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Sources and corrections

Sources last checked 2026-08-07

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