Question

For Exercises 11–22, find the mean, median, mode, and midrange. Then decide which you think is the most meaningful measure of average for that data set. For larger data sets, you should consider using technology.

Answer 1

The mean

To calculate the mean we must use the next equation,

$\begin{gathered} \bar{x}=\frac{\sum ^N_{i\mathop=1}X_i}{N} \\ \end{gathered}$

In this case, we must add all the amounts and then divide it by the number of months

$\bar{x}=5.3245$

The mean is 5.3245.

The median

To calculate the median we must organize the data and then take the data from the middle.

4,83

5,09

5,17

5,2

5,25

5,27

5,28

5,33

5,33

5,34

5,35

5,39

5,4

5,43

5,45

5,47

5,47

5,48

5,48

5,48

being a even number of data, we must take the two middle data and then we average them

$\frac{5.34+5.35}{2}=5.345$

The median is 5.345

The mode

The mode is the data that is repeated the most.

In this case, the mode is 5.48

The midrange

To calculate the midrange we must average the min value and the max value.

- min value: 4.83

- max value: 5.48

So, the midrange is

$\frac{4.83+5.48}{2}=5.155$

The midrange is 5.155

Decision:

To calculate the average, the most appropiate measure is the mean.