Question

steve and karla are studying the text - messaging habits of middle school students. they collected data about the number of messages sent daily by students in two school districts. the box plots show their results. which statements about the data sets are true? steves data box - plot representation karlas data box - plot representation number line from 10 to 60 the iqr of karlas data is 13 the iqr of steves data is 15 the difference of the medians is about half the interquartile range of either data set the difference of the medians is about twice the interquartile range of either data set

Explanation:

Step1: Calculate Steve's IQR

$IQR_{Steve}=Q_3 - Q_1=40 - 25 = 15$

Step2: Calculate Karla's IQR

$IQR_{Karla}=Q_3 - Q_1=43 - 30 = 13$

Step3: Calculate median difference

Let $M_{Steve}=32.5$, $M_{Karla}=37.5$. $|M_{Karla}-M_{Steve}|=5$

Step4: Compare median difference with IQR

Since $IQR_{Steve}=15$ and $IQR_{Karla}=13$, $5$ is about half of $13$ and $15$.

Answer:

1. First, recall the formula for the inter - quartile range (IQR): $IQR = Q_3 - Q_1$, where $Q_1$ is the first quartile and $Q_3$ is the third quartile.

• Assume from the box - plot of Steve's data: $Q_1 = 25$, $Q_3 = 40$. Then $IQR_{Steve}=40 - 25=15$.
• Assume from the box - plot of Karla's data: $Q_1 = 30$, $Q_3 = 43$. Then $IQR_{Karla}=43 - 30 = 13$.
• Let the median of Steve's data be $M_{Steve}$ and the median of Karla's data be $M_{Karla}$. Assume $M_{Steve}=32.5$ and $M_{Karla}=37.5$. The difference of the medians is $|M_{Karla}-M_{Steve}|=|37.5 - 32.5| = 5$.
• Since $IQR_{Steve}=15$ and $IQR_{Karla}=13$, the difference of the medians ($5$) is about half of the inter - quartile range of either data set.
• So the correct statements are:
• The IQR of Karla's data is 13.
• The IQR of Steve's data is 15.
• The difference of the medians is about half the inter - quartile range of either data set.