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.
121 122 126 129 132 136 139 140 142 143
147 148 148 150 151 156 158 158 162 167
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: \(121, 122, 126, 129, 132, 136, 139, 140, 142, 143, 147, 148, 148, 150, 151, 156, 158, 158, 162, 167\), the minimum \(Q_0=121\).

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

The data set \(n = 20\). The position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{20+1}{4}=5.25\).
The \(5^{th}\) value is \(132\) and the \(6^{th}\) value is \(136\). Using the formula \(Q_1=132+(136 - 132)\times0.25=132 + 1=133\).

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 \(10^{th}\) value is \(143\) and the \(11^{th}\) value is \(147\). So \(Q_2=\frac{143 + 147}{2}=145\).

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 \(15^{th}\) value is \(151\) and the \(16^{th}\) value is \(156\). Using the formula \(Q_3=151+(156 - 151)\times0.75=151+3.75 = 154.75\).

Step5: Find the maximum value

The maximum value is the largest number in the data set. So \(Q_4=167\).

Answer:

\(121,133,145,154.75,167\)