The Stem-and-leaf Plot Below Shows The Amount Of Tips Received By The Servers In A Restaurant In One Night.$[ \begin{tabular}{l|llllll} 0 & 9 & & & \ 1 & 2 & 4 & 7 & & \ 2 & 3 & 6 & 6 & 8 & \ 3 & 1 & 2 & 2 & 4 & 5 \ 5 & 9 & & & &

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Introduction

A stem-and-leaf plot is a type of data visualization tool used to display the distribution of a dataset. It is commonly used in statistics and data analysis to present numerical data in a clear and concise manner. 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.

Understanding the Stem-and-Leaf Plot

The stem-and-leaf plot is a two-column table where the left column represents the stem and the right column represents the leaves. The stem is the first digit of the data point, while the leaf is the last digit. For example, in the plot below, the stem for the data point 12 is 1, and the leaf is 2.

\[ \begin{tabular}{l|llllll} 0 & 9 & & & \\ 1 & 2 & 4 & 7 & & \\ 2 & 3 & 6 & 6 & 8 & \\ 3 & 1 & 2 & 2 & 4 & 5 \\ 5 & 9 & & & & \end{tabular}

Interpreting the Stem-and-Leaf Plot

To interpret the stem-and-leaf plot, we need to understand the distribution of the data points. The stem-and-leaf plot shows that the tips received by the servers range from 0 to 59. The most common tip amount is 9, which is the leaf for the stem 0. This suggests that the servers received a significant number of tips in the range of 0-9.

The stem-and-leaf plot also shows that there are several data points with leaves in the range of 1-9. This suggests that the servers received a moderate number of tips in the range of 10-29. The stem-and-leaf plot also shows that there are fewer data points with leaves in the range of 3-9. This suggests that the servers received fewer tips in the range of 30-59.

Calculating the Mean and Median

To calculate the mean and median of the data points, we need to first calculate the total sum of the data points. The total sum is calculated by multiplying each data point by its frequency and summing the results.

The total sum is calculated as follows:

(0 x 1) + (1 x 2) + (2 x 3) + (3 x 4) + (5 x 1) = 0 + 2 + 6 + 12 + 5 = 25

The mean is calculated by dividing the total sum by the total number of data points. The total number of data points is 15.

The mean is calculated as follows:

Mean = Total Sum / Total Number of Data Points = 25 / 15 = 1.67

The median is the middle value of the data points when they are arranged in order. Since there are 15 data points, the median is the 8th data point.

The median is calculated as follows:

Data Points in Order: 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 9 Median = 8th Data Point = 3

Calculating the Mode

The mode is the data point that appears most frequently in the dataset. To calculate the mode, we need to count the frequency of each data point.

The frequency of each data point is calculated as follows:

Data Point Frequency
0 1
1 2
2 3
3 4
4 2
5 1
6 2
9 1

The mode is the data point with the highest frequency. In this case, the mode is 3, which appears 4 times in the dataset.

Conclusion

In conclusion, the stem-and-leaf plot provides a clear and concise representation of the distribution of the data points. The plot shows that the tips received by the servers range from 0 to 59, with the most common tip amount being 9. The mean and median of the data points are 1.67 and 3, respectively. The mode is 3, which appears 4 times in the dataset. This analysis provides valuable insights into the distribution of the data points and can be used to inform business decisions.

Discussion

The stem-and-leaf plot is a useful tool for presenting numerical data in a clear and concise manner. It is commonly used in statistics and data analysis to display the distribution of a dataset. The plot provides a visual representation of the data points, making it easier to identify patterns and trends.

In this article, we have explored the stem-and-leaf plot below, which shows the amount of tips received by the servers in a restaurant in one night. We have calculated the mean and median of the data points, as well as the mode. This analysis provides valuable insights into the distribution of the data points and can be used to inform business decisions.

References

Appendix

The following is the R code used to calculate the mean and median of the data points:

# Load the data
data <- c(0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 9)

mean(data)



median(data)


**Stem-and-Leaf Plot Q&amp;A: Frequently Asked Questions**
=====================================================

**Q: What is a stem-and-leaf plot?**
--------------------------------

A: A stem-and-leaf plot is a type of data visualization tool used to display the distribution of a dataset. It is a two-column table where the left column represents the stem and the right column represents the leaves. The stem is the first digit of the data point, while the leaf is the last digit.

**Q: How do I create a stem-and-leaf plot?**
-----------------------------------------

A: To create a stem-and-leaf plot, you need to first arrange the data points in order. Then, you need to separate the stem and the leaf for each data point. The stem is the first digit of the data point, while the leaf is the last digit. You can then arrange the stems in order and list the corresponding leaves.

**Q: What is the purpose of a stem-and-leaf plot?**
---------------------------------------------

A: The purpose of a stem-and-leaf plot is to provide a clear and concise representation of the distribution of a dataset. It is commonly used in statistics and data analysis to display the distribution of a dataset.

**Q: How do I interpret a stem-and-leaf plot?**
---------------------------------------------

A: To interpret a stem-and-leaf plot, you need to understand the distribution of the data points. The stem-and-leaf plot shows the frequency of each data point, which can help you identify patterns and trends in the data.

**Q: What are the advantages of using a stem-and-leaf plot?**
---------------------------------------------------

A: The advantages of using a stem-and-leaf plot include:

* It provides a clear and concise representation of the distribution of a dataset.
* It is easy to create and interpret.
* It can help you identify patterns and trends in 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:

* It can be difficult to create a stem-and-leaf plot for large datasets.
* It can be difficult to interpret a stem-and-leaf plot for datasets with many outliers.

**Q: How do I calculate the mean and median from a stem-and-leaf plot?**
-------------------------------------------------------------------

A: To calculate the mean and median from a stem-and-leaf plot, you need to first calculate the total sum of the data points. The total sum is calculated by multiplying each data point by its frequency and summing the results. The mean is calculated by dividing the total sum by the total number of data points. The median is the middle value of the data points when they are arranged in order.

**Q: How do I calculate the mode 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. The mode is the data point with the highest frequency.

**Q: What are some common applications of stem-and-leaf plots?**
---------------------------------------------------------

A: Some common applications of stem-and-leaf plots include:

* Displaying the distribution of a dataset.
* Identifying patterns and trends in the data.
* Calculating the mean and median of the data points.
* Calculating the mode of the data points.

**Q: What are some common mistakes to avoid when creating a stem-and-leaf plot?**
-------------------------------------------------------------------------

A: Some common mistakes to avoid when creating a stem-and-leaf plot include:

* Not arranging the data points in order.
* Not separating the stem and the leaf for each data point.
* Not counting the frequency of each data point.

**Conclusion**
--------------

In conclusion, a stem-and-leaf plot is a useful tool for presenting numerical data in a clear and concise manner. It is commonly used in statistics and data analysis to display the distribution of a dataset. By understanding how to create and interpret a stem-and-leaf plot, you can gain valuable insights into the distribution of a dataset and make informed decisions.

**References**
--------------

* [1] Wikipedia. (2023). Stem-and-leaf plot. Retrieved from &lt;https://en.wikipedia.org/wiki/Stem-and-leaf_plot&gt;
* [2] Stat Trek. (2023). Stem-and-leaf plot. Retrieved from &lt;https://stattrek.com/stem-and-leaf-plot.aspx&gt;

**Appendix**
------------

The following is the R code used to calculate the mean and median of the data points:

```r
# Load the data
data &lt;- c(0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 9)

# Calculate the mean
mean(data)

# Calculate the median
median(data)
</code></pre>