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|4
1|55
2|4578
3|2

Answer 1

To find the mean, median, and mode(s) of the data represented in the stem-and-leaf plot, we first need to reconstruct the actual dataset based on the plot.

The stem-and-leaf plot is given as follows:

```
0 | 4
1 | 5 5
2 | 4 5 7 8
3 | 2
```

From this plot, we can list the numbers:

- From the stem `0`, the leaf `4` corresponds to the number **4**.
- From the stem `1`, the leaves `5 5` correspond to the numbers **15** and **15**.
- From the stem `2`, the leaves `4 5 7 8` correspond to the numbers **24**, **25**, **27**, and **28**.
- From the stem `3`, the leaf `2` corresponds to the number **32**.

Putting this all together, our dataset is:
\[ 4, 15, 15, 24, 25, 27, 28, 32 \]

### Step 1: Calculate the mean
The mean is calculated by taking the sum of all data points and dividing by the number of data points.

Sum of the data:
\[
4 + 15 + 15 + 24 + 25 + 27 + 28 + 32 = 150
\]

Number of data points:
\[
8
\]

Mean:
\[
\text{Mean} = \frac{150}{8} = 18.75
\]

### Step 2: Calculate the median
To find the median, we need to arrange the data in ascending order (already in order):
\[ 4, 15, 15, 24, 25, 27, 28, 32 \]

Since there are 8 data points (even number), the median will be the average of the 4th and 5th terms.

The 4th term is **24** and the 5th term is **25**.

Median:
\[
\text{Median} = \frac{24 + 25}{2} = \frac{49}{2} = 24.5
\]

### Step 3: Find the mode(s)
The mode is the number(s) that appear most frequently in the dataset.

From our dataset:
- **4** appears 1 time
- **15** appears 2 times
- **24** appears 1 time
- **25** appears 1 time
- **27** appears 1 time
- **28** appears 1 time
- **32** appears 1 time

The number **15** appears most frequently (2 times).

Thus, the mode is:
\[
\text{Mode} = 15
\]

### Summary of Results
- Mean: **18.75**
- Median: **24.5**
- Mode: **15**