Exercise 49 Page 9

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

2, 2, 4, 5, 6, 7, 7, 7, 8, 8

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 ten values in the set.

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

SubstituteValues

Substitute values

Mean = \frac{2 + 2 + 4 + 5 + 6 + 7 + 7 + 7 + 8 + 8}{1 0}

AddTerms

Add terms

Mean = \frac{5 6}{1 0}

CalcQuot

Calculate quotient

Mean = 5.6

Median

To identify the median, we observe the middle value.

2, 2, 4, 5, 6 ∣ 7, 7, 7, 8, 8

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,

6

and

7

are the most central values.

Median = \frac{6 + 7}{2} = 6.5

Mode

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

2, 2, 4, 5, 6, 7, 7, 7, 8, 8

We can see that

7

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