How do I find the mean, median, mode, and midrange of the following sample: 1,2,4,7,8,9,10,20?

Expert Answers

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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.

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