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# Mean, mode, median and range of the data set

When you get a set of data there are some terms to describe the data. The terms mean, median, and mode are different types of averages. Together with range, they describe our data set.

Mean - basic average of our data set, which is calculated by adding all data numbers and dividing them by total number of them.

Median - the middle number of the data set. To find the median, place the numbers of data set in value order. If there is an odd number of data numbers, then median is the middle number. If there is an even number of data numbers, then you need to add two middle numbers and divide by two.

Mode - the number that appears the most times in data set. Data set can have several modes, except all the numbers of data set appear the same number of times, then the data set has no modes. Having two modes data set is called bimodal. Having more than two modes data set is called multimodal.

Range - the difference between the highest and the lowest numbers from our given data set.

## Solved examples

Let's solve some example tasks to see how easy to find all values of these terms.

Find the mean, median, mode and range of the following data set: 1, 5, 18, 3, 8, 10, 18.

Mean: (1 + 5 + 18 + 3 + 8 + 10 + 18)/7 = 63/7 = 9
Now we put all the numbers in order: 1, 3, 5, 8, 10, 18, 18. Because we have odd number of data, the median is 8.
Because of two same numbers of 18, the mode is 18.
Range: 18 - 1 = 17

A TV watching time survey was conducted in the class. Here we have frequency table of TV watching time in hours per day: $$\begin{array}{|c|c|c|c|c|c|c|} \hline \text{TV time} & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text{Frequency} & 2 & 5 & 6 & 5 & 4 & 2 \\\hline \end{array}$$ Using this frequency table make tasks below: a) find the number of children in this class; b) find the range of this data set; c) find the mode of this data set; d) find the median of this data set; e) find the mean of this data set.

a) 2+5+6+5+4+2=24 b) Range = 5 - 0 = 5 c) Mode = 2 d) Median = 2 e) $$\bar{x}=\frac{0 \cdot 2+1 \cdot 5+2 \cdot 6+3 \cdot 5+4 \cdot 4+5 \cdot 2}{24}=\frac{58}{24}\approx 2.4$$

Note! For better understanding of this task, we can put all data table numbers in order: 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5. It will help easy to find all the terms we need.