The Stem-and-leaf Plot Below Shows The Amount Of Tips Received By The Servers In A Restaurant In One Night.$\[ \begin{tabular}{l|llllllll} 0 & 9 & & & & \\ 1 & 2 & 4 & 7 & & \\ 2 & & 3 & 6 & 6 & 8 & \\ 3 & 1 & 2 & 2 & 4 & 5 \\ 5 & 9 & & & &
Introduction
A stem-and-leaf plot is a graphical representation of a dataset that displays the distribution of the data. It is a useful tool for understanding the shape of the data, identifying patterns, and making inferences about the population. In this article, we will explore the stem-and-leaf plot below, which shows the amount of tips received by the servers in a restaurant in one night.
The Stem-and-Leaf Plot
{ \begin{tabular}{l|llllllll} 0 & 9 & & & & \\ 1 & 2 & 4 & 7 & & \\ 2 & & 3 & 6 & 6 & 8 & \\ 3 & 1 & 2 & 2 & 4 & 5 \\ 5 & 9 & & & & \end{tabular} }
Understanding the Plot
In the stem-and-leaf plot, the numbers on the left side of the vertical line are the stems, and the numbers on the right side are the leaves. The stem represents the tens digit of the data point, and the leaf represents the ones digit. For example, the data point 19 is represented by the stem 0 and the leaf 9.
Analyzing the Data
Let's analyze the data in the stem-and-leaf plot:
- The stem 0 has a leaf of 9, indicating that one server received a tip of $9.
- The stem 1 has leaves of 2, 4, and 7, indicating that three servers received tips of $12, $14, and $17, respectively.
- The stem 2 has leaves of 3, 6, 6, and 8, indicating that four servers received tips of $23, $26, $26, and $28, respectively.
- The stem 3 has leaves of 1, 2, 2, 4, and 5, indicating that five servers received tips of $31, $32, $32, $34, and $35, respectively.
- The stem 5 has a leaf of 9, indicating that one server received a tip of $59.
Calculating the Mean
To calculate the mean of the data, we need to add up all the data points and divide by the number of data points. Let's calculate the mean:
There are 14 data points, so the mean is:
Calculating the Median
To calculate the median of the data, we need to arrange the data points in order from smallest to largest and find the middle value. Let's arrange the data points:
Since there are 14 data points, the middle value is the 7th and 8th data points, which are both 26. Therefore, the median is 26.
Calculating the Mode
The mode is the data point that appears most frequently in the dataset. Let's count the frequency of each data point:
- 9: 1
- 12: 1
- 14: 1
- 17: 1
- 23: 1
- 26: 2
- 28: 1
- 31: 1
- 32: 2
- 34: 1
- 35: 1
- 59: 1
The data point 26 appears most frequently, with a frequency of 2. Therefore, the mode is 26.
Conclusion
In this article, we explored the stem-and-leaf plot below, which shows the amount of tips received by the servers in a restaurant in one night. We analyzed the data, calculated the mean, median, and mode, and drew conclusions about the distribution of the data. The stem-and-leaf plot is a useful tool for understanding the shape of the data and making inferences about the population.
Discussion
The stem-and-leaf plot is a graphical representation of a dataset that displays the distribution of the data. It is a useful tool for understanding the shape of the data, identifying patterns, and making inferences about the population. In this article, we explored the stem-and-leaf plot below, which shows the amount of tips received by the servers in a restaurant in one night.
Real-World Applications
The stem-and-leaf plot has many real-world applications, including:
- Business: Stem-and-leaf plots can be used to analyze sales data, customer satisfaction ratings, and employee performance.
- Science: Stem-and-leaf plots can be used to analyze experimental data, such as the results of a survey or the measurements of a physical phenomenon.
- Social Sciences: Stem-and-leaf plots can be used to analyze demographic data, such as the distribution of income or education levels.
Limitations
The stem-and-leaf plot has some limitations, including:
- Limited data: The stem-and-leaf plot is best suited for small to medium-sized datasets.
- Difficulty in interpreting: The stem-and-leaf plot can be difficult to interpret, especially for large datasets.
- Limited information: The stem-and-leaf plot only provides information about the distribution of the data, and does not provide information about the underlying causes of the data.
Conclusion
Q: What is a stem-and-leaf plot?
A: A stem-and-leaf plot is a graphical representation of a dataset that displays the distribution of the data. It is a useful tool for understanding the shape of the data, identifying patterns, and making inferences about the population.
Q: How is a stem-and-leaf plot created?
A: A stem-and-leaf plot is created by separating each data point into two parts: the stem and the leaf. The stem represents the tens digit of the data point, and the leaf represents the ones digit. For example, the data point 19 is represented by the stem 0 and the leaf 9.
Q: What are the advantages of using a stem-and-leaf plot?
A: The advantages of using a stem-and-leaf plot include:
- Easy to understand: Stem-and-leaf plots are easy to understand, even for those who are not familiar with statistical analysis.
- Visual representation: Stem-and-leaf plots provide a visual representation of the data, making it easier to identify patterns and trends.
- Quick analysis: Stem-and-leaf plots allow for quick analysis of the data, making it easier to make decisions based on the data.
Q: What are the disadvantages of using a stem-and-leaf plot?
A: The disadvantages of using a stem-and-leaf plot include:
- Limited data: Stem-and-leaf plots are best suited for small to medium-sized datasets.
- Difficulty in interpreting: Stem-and-leaf plots can be difficult to interpret, especially for large datasets.
- Limited information: Stem-and-leaf plots only provide information about the distribution of the data, and do not provide information about the underlying causes of the data.
Q: How is the mean calculated from a stem-and-leaf plot?
A: To calculate the mean from a stem-and-leaf plot, you need to add up all the data points and divide by the number of data points. For example, if the stem-and-leaf plot shows the following data points:
- 9
- 12
- 14
- 17
- 23
- 26
- 26
- 28
- 31
- 32
- 32
- 34
- 35
- 59
The mean would be calculated as follows:
There are 14 data points, so the mean is:
Q: How is the median calculated from a stem-and-leaf plot?
A: To calculate the median from a stem-and-leaf plot, you need to arrange the data points in order from smallest to largest and find the middle value. For example, if the stem-and-leaf plot shows the following data points:
- 9
- 12
- 14
- 17
- 23
- 26
- 26
- 28
- 31
- 32
- 32
- 34
- 35
- 59
The median would be calculated as follows:
- Arrange the data points in order from smallest to largest: 9, 12, 14, 17, 23, 26, 26, 28, 31, 32, 32, 34, 35, 59
- Since there are 14 data points, the middle value is the 7th and 8th data points, which are both 26. Therefore, the median is 26.
Q: How is the mode calculated from a stem-and-leaf plot?
A: To calculate the mode from a stem-and-leaf plot, you need to count the frequency of each data point. For example, if the stem-and-leaf plot shows the following data points:
- 9
- 12
- 14
- 17
- 23
- 26
- 26
- 28
- 31
- 32
- 32
- 34
- 35
- 59
The mode would be calculated as follows:
- Count the frequency of each data point:
- 9: 1
- 12: 1
- 14: 1
- 17: 1
- 23: 1
- 26: 2
- 28: 1
- 31: 1
- 32: 2
- 34: 1
- 35: 1
- 59: 1
- The data point 26 appears most frequently, with a frequency of 2. Therefore, the mode is 26.
Q: What are some real-world applications of stem-and-leaf plots?
A: Some real-world applications of stem-and-leaf plots include:
- Business: Stem-and-leaf plots can be used to analyze sales data, customer satisfaction ratings, and employee performance.
- Science: Stem-and-leaf plots can be used to analyze experimental data, such as the results of a survey or the measurements of a physical phenomenon.
- Social Sciences: Stem-and-leaf plots can be used to analyze demographic data, such as the distribution of income or education levels.
Q: What are some limitations of stem-and-leaf plots?
A: Some limitations of stem-and-leaf plots include:
- Limited data: Stem-and-leaf plots are best suited for small to medium-sized datasets.
- Difficulty in interpreting: Stem-and-leaf plots can be difficult to interpret, especially for large datasets.
- Limited information: Stem-and-leaf plots only provide information about the distribution of the data, and do not provide information about the underlying causes of the data.