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
121 123 125 128 129 133 134 137 139 142
146 147 148 150 152 155 158 158 160 167
the 5 - number summary is □,□,□,□, and □ 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: \(121, 123, 125, 128, 129, 133, 134, 137, 139, 142, 146, 147, 148, 150, 152, 155, 158, 158, 160, 167\), the minimum \(Q_0 = 121\).

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

First, find the median of the lower half of the data. The data set has \(n = 20\) values. The lower half is the first \(n/2=10\) values: \(121, 123, 125, 128, 129, 133, 134, 137, 139, 142\). The median of this lower - half (for \(n = 10\) (even number of data points)), \(Q_1=\frac{129 + 133}{2}=131\).

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

For \(n = 20\) (even number of data points), the median \(Q_2=\frac{142+146}{2}=144\).

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

The upper half of the data is the last \(n/2 = 10\) values: \(146, 147, 148, 150, 152, 155, 158, 158, 160, 167\). The median of this upper - half (for \(n = 10\) (even number of data points)), \(Q_3=\frac{152 + 155}{2}=153.5\).

Step5: Find the maximum value

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

Answer:

The 5 - number summary is \(121,131,144,153.5,167\)