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. 1.32 1.26 1.48 1.37 1.36 0.98 0.63 1.12 1.45 0.56 1.16 the 5 - number summary is \\( \square, \square \square \square \\) and \\( \square \\) all in w/kg. (use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Sort the data

Sort the given data in ascending order: \(0.56\), \(0.63\), \(0.98\), \(1.12\), \(1.16\), \(1.26\), \(1.32\), \(1.36\), \(1.37\), \(1.45\), \(1.48\)

Step2: Find the minimum

The minimum value is the first value in the sorted list. So, \(Min = 0.56\)

Step3: Find the first quartile (\(Q_1\))

For \(n = 11\) (odd number of data points), the position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{11+ 1}{4}=3\). The third value in the sorted list is \(Q_1=0.98\)

Step4: Find the median (\(Q_2\))

The position of the median is \(\frac{n + 1}{2}=\frac{11 + 1}{2}=6\). The sixth value in the sorted list is \(Median=1.26\)

Step5: Find the third quartile (\(Q_3\))

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3(11+1)}{4}=9\). The ninth value in the sorted list is \(Q_3 = 1.37\)

Step6: Find the maximum

The maximum value is the last value in the sorted list. So, \(Max=1.48\)

Answer:

\(0.56\), \(0.98\), \(1.26\), \(1.37\), \(1.48\)