Questions: Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for 7 customers at the bank. Here are the 7 waiting times (in minutes). 15,20,21,14,12,19,13 How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.

Solution Steps

To determine the modes of a data set, we need to identify the number(s) that appear most frequently. We will count the frequency of each number in the list and identify the number(s) with the highest frequency. If there is more than one number with the same highest frequency, the data set is multimodal.

The waiting times recorded are \( 15, 20, 21, 14, 12, 19, 13 \). Each of these values appears exactly once in the data set. Thus, the frequency of each waiting time is: \[ \text{Frequency} = \{15: 1, 20: 1, 21: 1, 14: 1, 12: 1, 19: 1, 13: 1\} \]

The maximum frequency among the waiting times is: \[ \text{max frequency} = 1 \]

Since all waiting times have the same maximum frequency of \( 1 \), every value in the data set is considered a mode. Therefore, the modes are: \[ \text{Modes} = \{15, 20, 21, 14, 12, 19, 13\} \]

The number of modes in this data set is \( 7 \), as there are seven distinct values.

Final Answer