Exercise 61 Page 31

We want to find the mean and median for the lengths of the bodies of jumping frogs. The first thing to do when finding the key features of a data set is rearranging the numbers from least to greatest. Let's do it!

20.3, 12.5, 7.6, 13.9, 9.2, 21.7 7.6, 17.5, 15.6, 14.1 ⇓ 7.6, 7.6, 9.2, 12.5, 13.9, 14.1 15.6, 17.5, 20.3, 21.7

Let's find the mean and median now.

Mean

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

10

values in the set, so we will divide the sum of the data set by

10 .

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

SubstituteValues

Substitute values

Mean = \frac{7 . 6 + 7 . 6 + 9 . 2 + 1 2 . 5 + 1 3 . 9 + 1 4 . 1 + 1 5 . 6 + 1 7 . 5 + 2 0 . 3 + 2 1 . 7}{1 0}

AddTerms

Add terms

Mean = \frac{1 4 0}{1 0}

CalcQuot

Calculate quotient

Mean = 14

The mean of the data set is

14

centimeters.

Median

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

7.6, 7.6, 9.2, 12.5, 13.9 ∣ 14.1 15.6, 17.5, 20.3, 21.7

Dang it! There is no middle value. When this happens, we calculate the median by finding the average of the two values closest to the middle. When arranged from least to greatest,

13.9

and

14.1

are the most central values, so let's find the average of these numbers.

Median = \frac{1 3 . 9 + 1 4 . 1}{2} = 14

The median of the data set is also

14

centimeters.