The mean shares the total equally: x= sum of valuesnumber of values. The median is the middle value after ordering; for an even count, average the two middle values. A mode is a most frequent value; more than one mode is possible. Example Order 12,7,5,3,5,7,5 to get 3,5,5,5,7,7,12. The total is 44, so the mean is 447 6.29, the median is the fourth value 5, and the mode is 5. The mean uses every value and is useful when the total matters. The median resists an isolated extreme value and often better describes a typical wage or waiting time. The mode identifies a most common category, such as shoe size, but need not be unique. Changing 12 to 120 changes the mean to 1527 21.7 while the median and mode stay 5. State which average supports a claim. For n ordered values, the median position is n+12 when n is odd; for even n, use positions n2 and n2+1. A position is not itself the data value.

The mean shares the total equally: \(\overline{x}=\dfrac{\text{sum of values}}{\text{number of values}}\). The median is the middle value after ordering; for an even count, average the two middle values. A mode is a most frequent value; more than one mode is possible.

Order \(12,7,5,3,5,7,5\) to get \(3,5,5,5,7,7,12\). The total is \(44\), so the mean is \(\dfrac{44}{7}\approx6.29\), the median is the fourth value \(5\), and the mode is \(5\).

The mean uses every value and is useful when the total matters. The median resists an isolated extreme value and often better describes a typical wage or waiting time. The mode identifies a most common category, such as shoe size, but need not be unique.

Changing \(12\) to \(120\) changes the mean to \(\dfrac{152}{7}\approx21.7\) while the median and mode stay \(5\). State which average supports a claim.

For \(n\) ordered values, the median position is \(\dfrac{n+1}{2}\) when \(n\) is odd; for even \(n\), use positions \(\dfrac n2\) and \(\dfrac n2+1\). A position is not itself the data value.

Mean, median and mode

Mean, median and mode