Question

Listed below are the measured radiation absorption rates​ (in W/kg) corresponding to 11 cell phones. Use the given data to construct a boxplot and identify the​ 5-number summary.

1.26 0.98 1.07 0.97 1.28 0.89 1.14 0.58 1.42 0.59 0.96

The 5-number summary is :_______

Answer 1

{ 0.58, 0.89, 0.98, 1.26, 1.42 }

Explanation:

We are given the data set { 1.26, 0.98, 1.07, 0.97, 1.28, 0.89, 1.14, 0.58, 1.42, 0.59, 0.96 }, consisting of 11 elements, each the radiation of 11 cell phones.

To construct the " 5 - number summary " the first thing we want to do is arrange the numbers from least to greatest, to find the median of the data set,

{ 0.58, 0.59, 0.89, 0.96, 0.97, 0.98, 1.07, 1.14, 1.26, 1.28, 1.42 }

The median of this data set is thus 0.98 W / kg. Mind you the units are not required here!

____

Now that we have the median, we can determine the first and third quartile, which are simply medians of the data set to the left and right of the median,

{ 0.58, 0.59, 0.89, 0.96, 0.97, 0.98, 1.07, 1.14, 1.26, 1.28, 1.42 }

`Q_1` = 0.89,
`Q_3` = 1.26

And of course the minimum and maximum of the data set are given to be 0.58, and 1.42

____

We have our 5 - number summary now! This includes the minimum, first quartile, median / second quartile, third quartile, and maximum values, in that order -

The 5 - number summary is { 0.58, 0.89, 0.98, 1.26, 1.42 }

And, your box and whisker plot is shown in the attachment below!