To analyze the data from the stem-and-leaf plot, let's first extract the values represented in the plot. The representation is as follows:
- Stem 0: 0|9 corresponds to the value 0.9 (or just 9).
- Stem 1: 1|59 corresponds to the values 1.5 and 1.9 (or just 15 and 19).
- Stem 2: 2|6788 corresponds to the values 2.6, 2.7, 2.8, and 2.8 (or just 26, 27, 28, 28).
- Stem 3: 3|1 corresponds to the value 3.1 (or just 31).
Now, let's compile the values into a list and sort them:
- Values: 9, 15, 19, 26, 27, 28, 28, 31
Step 1: Find the Mean
To find the mean, sum all the values and divide by the number of values.
\[ \text{Sum} = 9 + 15 + 19 + 26 + 27 + 28 + 28 + 31 = 183 \]
The number of values is 8.
\[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{183}{8} = 22.875 \]
Rounded to one decimal place, the mean is:
\[ \text{Mean} \approx 22.9 \]
Step 2: Find the Median
To find the median, we need to locate the middle value(s).
Since there are 8 values (an even number), the median will be the average of the 4th and 5th values when arranged in order.
The ordered list is: 9, 15, 19, 26, 27, 28, 28, 31
The 4th value is 26 and the 5th value is 27.
\[ \text{Median} = \frac{26 + 27}{2} = \frac{53}{2} = 26.5 \]
Step 3: Find the Mode(s)
To find the mode, identify the number(s) that appear most frequently.
In the list: 9, 15, 19, 26, 27, 28, 28, 31
The value 28 appears twice, while all other values appear once.
Thus, the mode is:
\[ \text{Mode} = 28 \]
Summary of Results
- Mean: 22.9
- Median: 26.5
- Mode(s): 28