English
Menu

What is Median?

The value in the middle when data are sorted by size. When there is an even number of values, it is the average of the two middle values. Unlike the mean, it is little affected by values far from the rest (outliers), so it suits as the representative value of data that include some extreme values, such as response times or incomes. Half of the data are at or below it and half at or above it, and it corresponds to the second quartile. The most frequent value is called the mode.

Japanese name: 中央値

Median appears in 5 practice questions across 4 topics, including Probability, Statistics and Queueing, Reliability, Data Structures and Algorithms.

Field: Probability, Statistics and Queueing

Try it: questions about Median

The response time of a server was measured 5 times, giving 20, 3, 5, 3 and 4 milliseconds in the order measured. Which of the following is the median of these data?

  1. A4 milliseconds
  2. B5 milliseconds
  3. C7 milliseconds
Show answer and explanation

Answer: A. 4 milliseconds

The median is the middle value when the data are sorted by size. Sorted, the data are 3, 3, 4, 5, 20, so the median is the third value, 4 milliseconds. The mean is 35 ÷ 5 = 7 milliseconds, pulled up by the single large value of 20 milliseconds. The median is a measure of central tendency that is little affected by such outliers, and the mode, the most frequent value, is 3 milliseconds.

The 11 data values 1, 3, 4, 6, 7, 8, 10, 12, 13, 15, 20 are shown in a box plot. The first and third quartiles are taken as the medians of the lower and upper halves of the data, excluding the median. Which of the following is the interquartile range, which corresponds to the length of the box?

  1. A4.5
  2. B9
  3. C19
Show answer and explanation

Answer: B. 9

The median is the sixth value, 8. The median of the lower half 1, 3, 4, 6, 7 is 4, the first quartile, and the median of the upper half 10, 12, 13, 15, 20 is 13, the third quartile, so the interquartile range is 13 − 4 = 9. A box plot draws a box from the first to the third quartile with a line at the median, showing where the middle half of the data lies. There are several conventions for computing quartiles, and the functions of spreadsheet software and the like may give slightly different values.

Median in the explanations

Questions that mention Median (5)

  1. The response time of a server was measured 5 times, giving 20, 3, 5, 3 and 4 milliseconds in the order measured. Which of the following is the median of these data?
  2. The 11 data values 1, 3, 4, 6, 7, 8, 10, 12, 13, 15, 20 are shown in a box plot. The first and third quartiles are taken as the medians of the lower and upper halves of the data, excluding the median. Which of the following is the interquartile range, which corresponds to the length of the box?
  3. Which statistical distribution is commonly used to describe the times to failure of many wires in electromigration life tests?
  4. Which is a typical case in which quicksort takes O(n²) time?
  5. When timing a program, why are measurements often repeated with the first few runs discarded?

Books on Probability, Statistics and Queueing Ad

As an Amazon Associate I earn from qualifying purchases.

Related terms

Quartile Electromigration Bayes' theorem Binomial distribution Conditional probability Confidence interval Correlation coefficient Expected value Exponential distribution Hypothesis testing

Back to the glossary