Chapter 7.3, Problem 1Q

To determine

The mean, median and mode of the given data set.

Answer to Problem 1Q

Mean = 3

Median = 3.25

Mode = 3.5

Best method to represent the data is median.

Explanation of Solution

Given:

The given data set is:

  $3\frac{1}{2},5,2\frac{1}{2},3,3\frac{1}{2},\frac{1}{2}$

Calculation:

The mean, median and mode of the given data can be calculated as:

Mean:

  $\begin{array}{l}=\frac{\frac{7}{2}+5+\frac{5}{2}+3+\frac{7}{2}+\frac{1}{2}}{6}\\ =3\end{array}$

Arrange the data set in ascending order to find the median:

  $0.5,2.5,3,3.5,3.5,5$

Median can be calculated by finding the middle value of the data set.

So, median is:

  $\begin{array}{l}=\frac{3+3.5}{2}\\ =\frac{6.5}{2}\\ =3.25\end{array}$

Mode is the data value in the data set that occurs most frequently.

Therefore, mode is 3.5 as it occurs twice.

The best method to represent the data is the median as mode is greater than most of the data in the data set and mean is smaller than most of the data.