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 leaf4corresponds to the number 4. - From the stem
1, the leaves5 5correspond to the numbers 15 and 15. - From the stem
2, the leaves4 5 7 8correspond to the numbers 24, 25, 27, and 28. - From the stem
3, the leaf2corresponds 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