Questions: Question The following is a list of prices, in dollars, of a water filter sold on an online store. is the mean, median, or mode likely to be the best measure of the center for the data set? 35,39,37,37,38,34,35,37,65 Select the correct answer below: Mode Mean Median

Solution Steps

The mean \( \mu \) of the data set is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

For the given data set \( 35, 39, 37, 37, 38, 34, 35, 37, 65 \):

\[ \mu = \frac{357}{9} \approx 39.67 \]

To find the median, we first sort the data:

\[ \text{Sorted data} = [34, 35, 35, 37, 37, 37, 38, 39, 65] \]

The formula for the rank of the median \( Q \) is:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (9 + 1) = 5.0 \]

The median corresponds to the value at position 5, which is:

\[ \text{Median} = 37 \]

The mode is the value that appears most frequently in the data set. In this case, the mode is:

\[ \text{Mode} = 37 \]

Given the presence of an outlier (65), the mean \( \mu \approx 39.67 \) is skewed. The median \( 37 \) is less affected by outliers and represents the middle value of the data set. The mode \( 37 \) also reflects the most common value.

Thus, the best measure of center for the data set is likely the median.

Final Answer