Questions: Englewood Health Center collected the following data on patients discharged on January 1, 2020. Which measure of central tendency would be most affected by Mallory's extremely long LOS? PATIENT NAME LENGTH OF STAY Ben 1 Josh 2 Emma 3 Bryan 4 Mallory 29 Taylor 2 Matthew 3 Aiden 2 Trevor 4 Tyler 2

Englewood Health Center collected the following data on patients discharged on January 1, 2020. Which measure of central tendency would be most affected by Mallory's extremely long LOS?

PATIENT NAME LENGTH OF STAY
Ben 1
Josh 2
Emma 3
Bryan 4
Mallory 29
Taylor 2
Matthew 3
Aiden 2
Trevor 4
Tyler 2

Transcript text: Englewood Health Center collected the following data on patients discharged on January 1, 2020. Which measure of central tendency would be most affected by Mallory's extremely long LOS? \begin{tabular}{|l|l|} \hline PATIENT NAME & LENGTH OF STAY \\ \hline Ben & 1 \\ \hline Josh & 2 \\ \hline Emma & 3 \\ \hline Bryan & 4 \\ \hline Mallory & 29 \\ \hline Taylor & 2 \\ \hline Matthew & 3 \\ \hline Aiden & 2 \\ \hline Trevor & 4 \\ \hline Tyler & 2 \\ \hline \end{tabular}

Solution

Solution Steps

To determine which measure of central tendency is most affected by Mallory's extremely long Length of Stay (LOS), we need to consider the mean, median, and mode. The mean is the average of all values, the median is the middle value when the data is ordered, and the mode is the most frequently occurring value. The mean is typically most affected by extreme values.

Step 1: Calculate the Mean

The mean is calculated by summing all the values and dividing by the number of values: \[ \text{mean} = \frac{1 + 2 + 3 + 4 + 29 + 2 + 3 + 2 + 4 + 2}{10} = \frac{52}{10} = 5.2 \]

Step 2: Calculate the Median

To find the median, we first sort the data: \[ \text{sorted data} = [1, 2, 2, 2, 2, 3, 3, 4, 4, 29] \] Since there are 10 values (an even number), the median is the average of the 5th and 6th values: \[ \text{median} = \frac{2 + 3}{2} = \frac{5}{2} = 2.5 \]

Step 3: Calculate the Mode

The mode is the value that appears most frequently in the data. From the sorted data, we see that the value 2 appears the most frequently (4 times): \[ \text{mode} = 2 \]

Step 4: Determine the Most Affected Measure of Central Tendency

Mallory's extremely long Length of Stay (29 days) significantly affects the mean, as it increases the average value. The median and mode are less affected by this extreme value.