To analyze the data provided in the stem-and-leaf plot, we will first recreate the dataset using the information given:
- From the stem "0|2", we have: \( 2 \)
- From the stem "1|46", we have: \( 14, 16 \)
- From the stem "2|4799", we have: \( 24, 27, 29, 29 \)
- From the stem "3|1", we have: \( 31 \)
So, the complete dataset is: \[ 2, 14, 16, 24, 27, 29, 29, 31 \]
Mean
To calculate the mean, we need to sum all the values and divide by the number of values.
Sum of the values: \[ 2 + 14 + 16 + 24 + 27 + 29 + 29 + 31 = 172 \] Number of values: There are \( 8 \) values.
Mean: \[ \text{Mean} = \frac{172}{8} = 21.5 \]
Median
To find the median, we need to order the dataset, which we already have in sorted order: \[ 2, 14, 16, 24, 27, 29, 29, 31 \]
Since there are \( 8 \) values (an even number), the median is the average of the two middle values. The middle values are the 4th and 5th numbers in the ordered dataset.
The 4th value is \( 24 \) and the 5th value is \( 27 \).
Median: \[ \text{Median} = \frac{24 + 27}{2} = \frac{51}{2} = 25.5 \]
Mode(s)
The mode is the number that appears most frequently in the dataset.
From the dataset:
- \( 2 \) appears \( 1 \) time
- \( 14 \) appears \( 1 \) time
- \( 16 \) appears \( 1 \) time
- \( 24 \) appears \( 1 \) time
- \( 27 \) appears \( 1 \) time
- \( 29 \) appears \( 2 \) times
- \( 31 \) appears \( 1 \) time
The mode is \( 29 \), as it appears most frequently (twice).
Summary of Results
- Mean: \( 21.5 \)
- Median: \( 25.5 \)
- Mode(s): \( 29 \)