Questions: A company's customer service hotline handles many calls relating to orders, refunds, and other issues. The company's records indicate that the median length of calls to the hotline is 4.4 minutes with an IQR of 2.3 minutes. a) If the company were to describe the duration of these calls in seconds instead of minutes, what would the median and IQR be? b) In an effort to speed up the customer service process, the company decides to streamline the series of pushbutton menus customers must navigate, cutting the time by 30 seconds. What will the median and IQR of the length of hotline calls become? a) The new median will be seconds. The new IQR will be seconds. (Type integers or decimals. Do not round.)

Solution Steps

To solve the given problem, we need to perform unit conversions and simple arithmetic operations:

a) Convert the median and IQR from minutes to seconds by multiplying each by 60, since there are 60 seconds in a minute.

b) Adjust the median by subtracting 30 seconds to account for the streamlined process. The IQR remains unchanged because it is a measure of spread and not affected by a constant shift.

To convert the median and interquartile range (IQR) from minutes to seconds, we multiply each by 60, since there are 60 seconds in a minute.

\[ \text{Median in seconds} = 4.4 \, \text{minutes} \times 60 = 264.0 \, \text{seconds} \]

\[ \text{IQR in seconds} = 2.3 \, \text{minutes} \times 60 = 138.0 \, \text{seconds} \]

The company decides to streamline the process, reducing the call time by 30 seconds. This affects the median but not the IQR, as the IQR is a measure of spread and remains unchanged by a constant shift.

\[ \text{New median in seconds} = 264.0 \, \text{seconds} - 30 = 234.0 \, \text{seconds} \]

The IQR remains:

\[ \text{New IQR in seconds} = 138.0 \, \text{seconds} \]

Final Answer