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

1, 29, 30, 31, 33, 33

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{1 + 2 9 + 3 0 + 3 1 + 3 3 + 3 3}{6}

AddTerms

Add terms

Mean = \frac{1 5 7}{6}

CalcQuot

Calculate quotient

Mean = 26.166666 \dots

RoundDec

Round to $3$ decimal place(s)

Mean \approx 26.167

Median

To identify the median, we observe the middle value.

1, 29, 30 ∣ 31, 33, 33

Dangit! 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,

30

and

31

are the most central values.

Median = \frac{3 0 + 3 1}{2} = 30.5

Mode

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

1, 29, 30, 31, 33, 33

We can see that

33

occurs more frequently than any other value in the set, so this is the mode.

Which Measure Is Best?

For the given scenario, the best measure is the median because mean is less than the most of the data points. Outliers affect the mean but not the median. We have an outlier and most frequent value is the greatest in the data set, so both of mean and mode does not describe the central tendency as good as median does in this example.

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