Question

Find the mean, median, and mode(s) of the data in the following stem-and-leaf plot. The leaf represents the ones digit.

0|2
1|68
2|4489
3|2

Answer 1

To analyze the given stem-and-leaf plot, we first need to extract the actual data that it represents.

The plot is formatted as follows:

- **Stem** represents the tens place.
- **Leaf** represents the ones place.

From the given stem-and-leaf plot:

- **0 | 2** means 2 (i.e., 02)
- **1 | 68** means 16 and 18
- **2 | 4489** means 24, 24, 28, and 29
- **3 | 2** means 32

Now let's list all the numbers from the plot:

- From the stem 0: 2
- From the stem 1: 16, 18
- From the stem 2: 24, 24, 28, 29
- From the stem 3: 32

So, the complete list of data is:

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

### Mean

To calculate the mean, we first add all the numbers together:

\[
2 + 16 + 18 + 24 + 24 + 28 + 29 + 32 = 2 + 16 + 18 + 24 + 24 + 28 + 29 + 32 = 173
\]

Now, we divide the total sum by the number of data points (which is 8):

\[
\text{Mean} = \frac{173}{8} = 21.625
\]

### Median

The median is the middle value when the numbers are arranged in order.

The ordered list of numbers is:

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

Since there are 8 numbers (an even count), the median will be the average of the 4th and 5th numbers:

\[
\text{4th number} = 24, \quad \text{5th number} = 24
\]

\[
\text{Median} = \frac{24 + 24}{2} = \frac{48}{2} = 24
\]

### Mode

The mode is the number that appears most frequently in the data.

In our list:

- 2 appears once
- 16 appears once
- 18 appears once
- 24 appears twice
- 28 appears once
- 29 appears once
- 32 appears once

The number that appears most frequently is 24.

### Summary of Results:

- **Mean**: 21.625
- **Median**: 24
- **Mode**: 24