QuestionCustomers 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 19 customers at the bank. Here are the 19 waiting times (in minutes).
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Answer the questions below.
\begin{tabular}{|l|l|}
\hline (a) For these data, which measures of & Mean \\
central tendency take more than one value? & Median \\
Choose all that apply. & Mode \\
\hline \begin{tabular}{l}
(b) Suppose that the measurement 37 \\
largest measurement in the data set) were
\end{tabular} & Mone of these measures \\
\hline
\end{tabular}
Studdy Solution
STEP 1
1. We have a data set of 19 waiting times: .
2. We need to determine which measures of central tendency (mean, median, mode) can take more than one value.
3. We need to consider the effect of removing the largest measurement (37) on these measures.
STEP 2
1. Calculate the mean, median, and mode of the original data set.
2. Determine which measures can take more than one value.
3. Recalculate the mean, median, and mode after removing the largest measurement (37).
4. Analyze the effect of removing the largest measurement on these measures.
STEP 3
Calculate the mean of the original data set:
STEP 4
Calculate the median of the original data set. Since there are 19 data points, the median is the 10th value:
STEP 5
Identify the mode(s) of the original data set. The mode is the most frequently occurring value(s):
STEP 6
Determine which measures can take more than one value. In this context, only the mode can have more than one value if there are multiple values with the same highest frequency.
STEP 7
Remove the largest measurement (37) and recalculate the mean:
STEP 8
Recalculate the median of the new data set. With 18 data points, the median is the average of the 9th and 10th values:
STEP 9
Recalculate the mode(s) of the new data set. The mode remains the same:
STEP 10
Analyze the effect of removing the largest measurement. The mean and median have changed, but the mode remains the same. The mode is still the measure that can take more than one value.
The measures of central tendency that can take more than one value are:
- Mode
Removing the largest measurement affects the mean and median but not the mode.
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