The first thing that should be done when finding the key features of a data set is rearranging the numbers from least to greatest.

36, 82, 82, 83, 86, 94

Let's proceed to finding the mean, median, and mode.

Mean

The mean of a data set is calculated by finding the sum of all values in the set and then dividing by the number of values in the set. In this case, there are

6

values in the set.

Mean = \frac{Sum of values}{Number of values}

SubstituteValues

Substitute values

Mean = \frac{3 6 + 8 2 + 9 4 + 8 3 + 8 6 + 8 2}{6}

AddTerms

Add terms

Mean = \frac{4 9 3}{6}

CalcQuot

Calculate quotient

Mean = 77.1 \overline{6}

RoundDec

Round to $1$ decimal place(s)

Mean \approx 77.2

Median

To identify the median, we observe the middle value.

36, 82, 82 ∣ 83, 86, 94

Notice that there is no middle value. When this happens, we need to calculate the median by finding the average of the two values closest to the middle. When arranged from least to greatest,

82

and

83

are the most central values.

Median = \frac{8 2 + 8 3}{2} = 82.5

Mode

The mode of a data set is the value that occurs most frequently.

36, 82, 82, 83, 86, 94

We can see that

82

occurs more frequently than the other values, so there is one mode in this set.

Which Measure Is Best?

Recall that the mean is highly influenced by values that are way greater or smaller than the rest of the values. Therefore, since $36$ is much smaller than the rest of the values, the mean is not a good measure of the data. In this case, the best measure is the median. Another good measure would be the mode because it occurs the most frequently within the data.

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