Given the data set 1,2,4,7,8,9,10,20:

(1) The mean (arithmetic mean) is the sum of the data divided by the number, n, of pieces of data.

` bar(x)=(1+2+4+7+8+9+10+20)/8=61/8=7.625 `

Usually you report the mean to one more digit than the given data so `bar(x)=7.6 `

(2) The median is the number in the middle of the **ordered** data set. I.e. there are as many data points below the median as above the median.

Here the median is between 7 and 8; in the case that there is an even number of data points you take the mean of the two in the middle.

`"med"=(7+8)/2=7.5 `

(3) The mode is the datum that occurs the most often. A set can have no mode, 1 mode, or multiple modes. Here no number occurs more than once.

**There is no mode.**

(4) The midrange is the mean of the largest and smallest data points.

`"midrange"=(20+1)/2=10.5 `

These are all called measures of central tendency or measures of the middle.

**Further Reading**

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