BUILDING & PLANNING · FIELD TOOL
The median is the middle value once the numbers are sorted. For 7, 1, 3, 9, 4 and 6, sort them to 1, 3, 4, 6, 7, 9; with an even count, take the average of the two middle values: (4 + 6) ÷ 2 = 5. With an odd count, the median is simply the middle one. One extreme value does not pull the median the way it pulls the mean.
Results update as you type.
Check the working before you order.
| Sorted | 1, 3, 4, 6, 7, 9 |
| Count | 6 |
| Position of the median | between values 3 and 4 |
| Mean, for comparison | 5 |
| Mode | none |
| Quartiles Q1 and Q3 | 3 and 7 |
Your prices are remembered on this device only.
Results are estimates for planning and material ordering only. They are not a substitute for structural design or approval by a qualified engineer. Read the full disclaimer.
Sort the values
Odd n: median = value number (n + 1) ÷ 2
Even n: median = average of values n ÷ 2 and n ÷ 2 + 17, 1, 3, 9, 4, 6:
| Values | Median | Mean |
|---|---|---|
| 1, 3, 4, 6, 7, 9 | 5 | 5 |
| 2, 4, 9 | 4 | 5 |
| 10,000, 10,500, 11,000, 25,000 | 10,750 | 14,125 |
| 5, 5, 5, 5, 50 | 5 | 14 |
Sort the numbers from smallest to largest. With an odd count, the median is the middle value; with an even count, it is the average of the two middle values.
The average of the two in the middle. For 1, 3, 4, 6, 7, 9 the middle two are 4 and 6, so the median is 5.
When a few values are far from the rest. Quotes of 10,000, 10,500, 11,000 and 25,000 have a mean of 14,125 but a median of 10,750, which is closer to a typical quote.
At position (n + 1) ÷ 2 in the sorted list. For 9 values that is the 5th; for 10 values it falls between the 5th and 6th.
The medians of the lower and upper halves. Q1 has a quarter of the values below it and Q3 has three quarters below it.