Questions: Find the mean, median, and mode for the following data set. 47, 27, 38, 66, 66, 96 Part 1 of 3 (a) Find the mean. Round your answer to one decimal place, if necessary. Mean = Part 2 of 3 (b) Find the median. Round your answer to one decimal place, if necessary. Median =

Solution Steps

To find the mean \( \mu \) of the data set, we use the formula:

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

where \( N \) is the number of data points and \( x_i \) are the individual data points. For the given data set \( \{47, 27, 38, 66, 66, 96\} \):

\[ \mu = \frac{47 + 27 + 38 + 66 + 66 + 96}{6} = \frac{340}{6} \approx 56.7 \]

Thus, the mean is:

\[ \text{Mean} = 56.7 \]

To find the median, we first sort the data set:

\[ \text{Sorted data} = [27, 38, 47, 66, 66, 96] \]

Since there are \( N = 6 \) data points (an even number), the median \( Q \) is calculated using the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (6 + 1) = 3.5 \]

This indicates that the median is the average of the values at ranks 3 and 4:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{47 + 66}{2} = \frac{113}{2} = 56.5 \]

Thus, the median is:

\[ \text{Median} = 56.5 \]

Final Answer