Question

listed below are amounts of strontium - 90 (in millibecquerels, or mbq) in a simple random sample of baby teeth obtained from residents in a region born after 1979. use the given data to construct a boxplot and identify the 5 - number summary.
128 130 134 137 139 143 143 144 146 148
150 150 151 153 156 161 162 163 166 173
the 5 - number summary is \\( \square, \square, \square, \square \\), and \\( \square \\), all in mbq.
(use ascending order. type integers or decimals. do not round)

Explanation:

Step1: Find the minimum value

The minimum value is the smallest number in the data set. Looking at the data: \(128,130,134,137,139,143,143,144,146,148,150,150,151,153,156,161,162,163,166,173\)
The minimum value \(Q_0 = 128\)

Step2: Find the first quartile (\(Q_1\))

The data set has \(n = 20\) values. The position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{20+ 1}{4}=5.25\)
The first \(5\) values are \(128,130,134,137,139\). Using linear - interpolation: \(Q_1=139+(143 - 139)\times0.25=140\)

Step3: Find the median (\(Q_2\))

The position of the median for \(n = 20\) (even number of data points) is \(\frac{n}{2}=10\) and \(\frac{n}{2}+1 = 11\). The median \(Q_2=\frac{148 + 150}{2}=149\)

Step4: Find the third quartile (\(Q_3\))

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75\)
The first \(15\) values are \(128,130,134,137,139,143,143,144,146,148,150,150,151,153,156\). Using linear - interpolation: \(Q_3=161+(162 - 161)\times0.75 = 161.75\)

Step5: Find the maximum value

The maximum value is the largest number in the data set. The maximum value \(Q_4=173\)

Answer:

\(128\), \(140\), \(149\), \(161.75\), \(173\)