English
All three averages plus range and quartiles, with how each was found.
Last updated
The Coddy math course teaches the method itself - you work each step on an interactive board and get told exactly where a move went wrong.
The mean adds everything and shares it out equally. The median ignores the sizes and picks the value in the middle of the order. The mode ignores position entirely and picks whatever occurs most often. They are three genuinely different questions, and on a lopsided list they give three genuinely different answers - which is exactly when knowing the difference matters.
That is why one house price in a street of flats moves the mean and leaves the median alone: the mean feels every value's size, while the median only counts positions. Ask which "average" you were given whenever a single number is quoted about incomes, prices or waiting times - the choice is doing real work.
This page reports all three, plus the range, the quartiles and the interquartile range, and shows how each one was found from the sorted list. The means stay exact: the mean of 1, 2 and 4 is 7/3 here, not 2.33, because 2.33 is a different number and rounding is a decision the reader should get to make.
Smallest to largest. This costs a minute and makes three of the answers readable at a glance.
Add every value, then divide by how many there are. Keep it as a fraction if it does not come out whole - 7/3 is exact and 2.33 is not.
With an odd count it is the single middle value. With an even count, take the two middle values and average them.
The value that appears most often. Tally as you go through the sorted list; ties are real and both count.
Largest minus smallest is the range. Split the sorted list at the median (leaving the median out if the count is odd) and take the median of each half: those are Q1 and Q3, and Q3 − Q1 is the interquartile range.
Notice the rows where they disagree - a skewed list is exactly where the choice of average changes the story.
| Values | Mean | Median | Mode | Range |
|---|---|---|---|---|
| 2, 4, 4, 4, 5, 5, 7, 9 | 5 | 4.5 | 4 | 7 |
| 1, 2, 3, 4 | 2.5 | 2.5 | none | 3 |
| 12, 15, 11, 15, 20 | 14.6 | 15 | 15 | 9 |
| 1, 2, 4 | 7/3 | 2 | none | 3 |
| 1, 1, 2, 2, 3 | 1.8 | 2 | 1 and 2 | 2 |
| 10, 10, 10, 100 | 32.5 | 10 | 10 | 90 |
| 3, 3, 3 | 3 | 3 | 3 | 0 |
| 5, 6, 7, 8, 9 | 7 | 7 | none | 4 |
2, 4, 4, 4, 5, 5, 7, 9The total is 40 over 8 values, so the mean is 5. With an even count the median is the average of the 4th and 5th values, 4 and 5, giving 4.5. The mode is 4, which appears three times. Three different numbers, all correct answers to different questions.
1, 2, 3, 4Every value appears exactly once, so there is no mode at all - not zero, and not the first value. The mean and median are both 2.5, which happens whenever the list is evenly spread. The median here is not a member of the list, and that is perfectly normal for an even count.
1, 1, 2, 2, 3Both 1 and 2 appear twice, so this list is bimodal and both are modes. Picking one and discarding the other is a mistake; the honest answer is both. The mean is 1.8 and the median is 2.
10, 10, 10, 100The median is 10 and the mode is 10, but the mean is 32.5 - more than three times what most of the data says. This is the property that makes the median the honest choice for house prices and salaries, and the mean the misleading one.
1, 2, 4The total is 7 over 3 values, so the mean is 7/3 - and 7/3 is what this page reports. Writing 2.33 rounds a third away, which matters the moment the number is used in anything else, such as a standard deviation.
