Questions: Find the mean, median, and mode(s) of the data in the following stem-and-leaf plot. 0 2 1 68 2 4489 3 2 Part 1 of 3 Find the mean. Round your answer to one decimal place, if necessary. Mean: Part 2 of 3 Find the median. Round your answer to one decimal place, if necessary. Median:

Solution Steps

From the given stem-and-leaf plot, we extract the data points as follows:

\[ \text{Stem} \, 0: \, 2 \quad \Rightarrow \quad 2 \] \[ \text{Stem} \, 1: \, 6, 8 \quad \Rightarrow \quad 16, 18 \] \[ \text{Stem} \, 2: \, 4, 4, 8, 9 \quad \Rightarrow \quad 24, 24, 28, 29 \] \[ \text{Stem} \, 3: \, 2 \quad \Rightarrow \quad 32 \]

Thus, the complete dataset is:

\[ \{2, 16, 18, 24, 24, 28, 29, 32\} \]

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

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

Where \( N \) is the number of data points. Here, \( N = 8 \) and the sum of the data points is \( 173 \):

\[ \mu = \frac{173}{8} = 21.6 \]

To find the median, we first determine the rank using the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (8 + 1) = 4.5 \]

Since the rank is not an integer, we take the average of the values at ranks 4 and 5:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{24 + 24}{2} = 24.0 \]

Final Answer