Question

a meteorologist collected annual rainfall records for three towns. the boxplots above show the results. the range of a data set is the difference between the minimum and maximum. determine the range in annual rainfall for the three towns. town a: 23 cm town b: 12 cm town c: 11 cm the interquartile range or iqr of a data set is the difference between the the first and third quartiles. determine the iqr in annual rainfall for the three towns. town a: cm town b: cm town c: 5 cm which town has the lowest first quartile value? town a which town has the highest third quartile value? town b question help: read message instructor

Explanation:

Step1: Determine the first and third quartiles for Town A

From the box - plot, for Town A, the first quartile \(Q_1 = 10\) and the third quartile \(Q_3=22\).

Step2: Calculate the IQR for Town A

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\).
Substitute \(Q_1 = 10\) and \(Q_3 = 22\) into the formula: \(IQR=22 - 10=12\).

Step3: Determine the first and third quartiles for Town B

From the box - plot, for Town B, the first quartile \(Q_1 = 12\) and the third quartile \(Q_3 = 22\).

Step4: Calculate the IQR for Town B

Using the formula \(IQR = Q_3-Q_1\), substitute \(Q_1 = 12\) and \(Q_3 = 22\): \(IQR=22 - 12 = 10\).

Answer:

Town A: \(12\) cm, Town B: \(10\) cm