Questions: Find the mean, median, and mode for the following data set. Round your answers to one decimal place, if necessary. 11 24 24 -13 14

Solution Steps

To find the mean \( \mu \) of the data set \( \{11, 24, 24, -13, 14\} \), we use the formula:

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

where \( N \) is the number of data points. Here, \( N = 5 \) and the sum of the data points is:

\[ \sum_{i=1}^5 x_i = 11 + 24 + 24 - 13 + 14 = 60 \]

Thus, the mean is calculated as:

\[ \mu = \frac{60}{5} = 12.0 \]

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

\[ \text{Sorted data} = \{-13, 11, 14, 24, 24\} \]

The median is the value at the position given by the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (5 + 1) = 3.0 \]

Since the rank is 3.0, the median corresponds to the value at position 3 in the sorted data, which is:

\[ \text{Median} = 14 \]

Final Answer