Question

a researcher for the epa measured the amount of arsenic in the water near a sewage treatment plant. over 5 days, they took n = 20 measurements (in ppb). their sample data is summarized in the ogive graph shown below. what is the median amount of arsenic? 45 × ppb what is the iqr of arsenic? 20 √ ppb question help: ▶ video □ message instructor

Explanation:

Step1: Recall median formula for $n = 20$

For $n = 20$ (even - numbered data set), median is average of $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered - data values. Here, $\frac{n}{2}=10$ and $\frac{n}{2}+1 = 11$. We use the ogive to find the values corresponding to cumulative frequencies 10 and 11.

Step2: Read from ogive

On the ogive, find the arsenic values corresponding to cumulative frequencies 10 and 11. The cumulative - frequency of 10 and 11 occurs at an arsenic value of 45 ppb. So the median is 45 ppb.

Step3: Recall IQR formula

The inter - quartile range $IQR=Q_3 - Q_1$. For $n = 20$, $Q_1$ is the value at the $\frac{n}{4}=5$th ordered data value and $Q_3$ is the value at the $\frac{3n}{4}=15$th ordered data value.

Step4: Read $Q_1$ and $Q_3$ from ogive

From the ogive, the value at the 5th cumulative - frequency is 35 ppb ($Q_1$) and the value at the 15th cumulative - frequency is 55 ppb ($Q_3$). Then $IQR = Q_3 - Q_1=55 - 35=20$ ppb.

Answer:

Median: 45 ppb
IQR: 20 ppb