Exercise 33 Page 201

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

8, 22, 19, 12, 18, 19, 10, 35, 12, 19, 16, 21 ⇓ 8, 10, 12, 12, 16, 18, 19, 19, 19, 21, 22, 35

To identify the median, we look for the middle value.

8, 10, 12, 12, 16, 18 ∣ 19, 19, 19, 21, 22, 35

Dang it! 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,

18

and

19

are the most central values. Let's average them.

Median = \frac{1 8 + 1 9}{2} = 18.5

The median of the data is

18.5

minutes.

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.

8, 22, 19, 12, 18, 19, 10, 35, 12, 19, 16, 21

In this case, there are

12

values in the set. Let's add up the values and divide by

12 .

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

SubstituteValues

Substitute values

Mean = \frac{8 + 2 2 + 1 9 + 1 2 + 1 8 + 1 9 + 1 0 + 3 5 + 1 2 + 1 9 + 1 6 + 2 1}{1 2}

AddTerms

Add terms

Mean = \frac{2 1 1}{1 2}

The mean of the data set is

\frac{2 1 1}{1 2}

minutes. We can also write this fraction as a mixed number.

Mean = \frac{2 1 1}{1 2}

WriteSum

Write as a sum

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

WriteSumFrac

Write as a sum of fractions

\frac{2 0 4}{1 2} + \frac{7}{1 2}

CalcQuot

Calculate quotient

17 + \frac{7}{1 2}

AddTerms

Add terms

17 \frac{7}{1 2}

The mean of the data set is

17 \frac{7}{1 2}

minutes.

Subchapter links

4.2.1 Recognizing Proportional Relationships p.201

4.2.2 Proportional Relationships with Tables and Graphs p.205-206

4.2.3 Unit Rate and Proportional Equations p.211

4.2.4 Connecting Representations of Proportional Relationships p.214-216