Question

The following are the distances (in miles) to the nearest airport for 13 families.10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39Notice that the numbers are ordered from least to greatest.Give the five-number summary and the interquartile range for the data set.

Answer 1

We have the next given set for distances (in miles) to the nearest for 13airport families:

10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39

The minimum is the least number value. Then:

Minimum =10

In this case, we have 13 data, so :

- The middle number is the median:

10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39

Now, the lower quartile is given by the next equation:

`=(n+1)\ast(1)/(4)`

Replacing:

`\begin{gathered} =(13+1)\ast(1)/(4) \\ =14\ast(1)/(4) \\ =3.5=4 \end{gathered}`

The lower quartile is in the fourth position:

Lower quartile = 15

The upper quartile is given by the next equation:

`\begin{gathered} =(n+1)\ast(3)/(4) \\ =(13+1)\ast(3)/(4) \\ =10.5=11 \end{gathered}`

The upper quartile is located in the 11th position:

Upper quartile = 34

The interquartile range is given by:

IQR=upper quartile - lower quartile

IQR=34-15

The interquartile range =19