Median of a Data Set: Public Worked Question

Question

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

B. $17$

1The values are already ordered: $9, 12, 14, 20, 25, 28$ , and there are $6$ of them.
2With an even count, the median is the mean of the two middle values, here the third and fourth: $14$ and $20$ .
3Average them: $(14 + 20) \div 2 = 34 \div 2 = 17$ , which differs from the mean of $18$ .

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

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

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

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

\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.

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

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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