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
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