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. 125 128 130 133 134 138 139 142 144 145 147 147 149 152 155 158 161 163 166 171 the 5 - number summary is □,□,□,□, and □, all in mbq. (use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Find the minimum

The minimum value in the data - set is the smallest number.
125

Step2: Find the first quartile ($Q_1$)

There are $n = 20$ data points. The position of $Q_1$ is $L_{Q_1}=\frac{n + 1}{4}=\frac{20+1}{4}=5.25$. So, $Q_1$ is the value $0.25$ of the way between the 5th and 6th ordered data - points. The 5th value is 134 and the 6th value is 138. $Q_1=134+(138 - 134)\times0.25=135$.

Step3: Find the median ($Q_2$)

The position of the median for $n = 20$ (an even - numbered data set) is $L_{Q_2}=\frac{n}{2}=10$ and $\frac{n}{2}+1 = 11$. The median is the average of the 10th and 11th ordered data - points. The 10th value is 145 and the 11th value is 147. $Q_2=\frac{145 + 147}{2}=146$.

Step4: Find the third quartile ($Q_3$)

The position of $Q_3$ is $L_{Q_3}=\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75$. So, $Q_3$ is the value $0.75$ of the way between the 15th and 16th ordered data - points. The 15th value is 155 and the 16th value is 158. $Q_3=155+(158 - 155)\times0.75=157.25$.

Step5: Find the maximum

The maximum value in the data - set is the largest number.
171

Answer:

125, 135, 146, 157.25, 171