Select The Correct Answer.Becky Is An Experienced Swimmer. The Table Contains Data On Her Times In The 100-meter Freestyle Event For Each Year Over The Past Six Years.$[ \begin{tabular}{|c|c|} \hline Year & \text{Time (seconds)} \ \hline 1 & 98

Introduction

In this article, we will delve into the world of statistics and explore how to analyze time data. We will use a real-world example to demonstrate how to apply statistical concepts to a practical problem. Our goal is to determine the correct answer to a question based on the given data.

The Problem

Becky is an experienced swimmer, and we have data on her times in the 100-meter freestyle event for each year over the past six years. The table below contains the data:

Understanding the Data

Before we can analyze the data, we need to understand what it represents. The data is in the form of a time series, where each observation represents the time taken by Becky to complete the 100-meter freestyle event in a particular year. The data is also ordered chronologically, with the earliest year first.

Descriptive Statistics

To get a better understanding of the data, we can calculate some basic descriptive statistics. These include the mean, median, mode, and standard deviation.

• Mean: The mean is the average of all the observations. To calculate the mean, we add up all the values and divide by the number of observations.

  $\text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n}$

  where $x_i$ is the $i^{th}$ observation and $n$ is the number of observations.

  In this case, the mean is:

  $\text{Mean} = \frac{98 + 95 + 92 + 90 + 88 + 86}{6} = 91.17$

• Median: The median is the middle value of the data when it is arranged in order. If there are an even number of observations, the median is the average of the two middle values.

  In this case, the median is:

  $\text{Median} = 90$

• Mode: The mode is the value that appears most frequently in the data.

  In this case, there is no mode, as each value appears only once.

• Standard Deviation: The standard deviation is a measure of the spread of the data. It is calculated as the square root of the variance.

  $\text{Standard Deviation} = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \text{Mean})^2}{n}}$

  In this case, the standard deviation is:

  $\text{Standard Deviation} = \sqrt{\frac{(98-91.17)^2 + (95-91.17)^2 + (92-91.17)^2 + (90-91.17)^2 + (88-91.17)^2 + (86-91.17)^2}{6}} = 3.51$

Interpretation

Now that we have calculated the descriptive statistics, we can interpret the results. The mean time taken by Becky to complete the 100-meter freestyle event is 91.17 seconds, with a standard deviation of 3.51 seconds. This means that the times are spread out over a range of 6.68 seconds (from 84.47 seconds to 98 seconds).

Conclusion

In this article, we have analyzed the time data of Becky's 100-meter freestyle event over the past six years. We have calculated the mean, median, mode, and standard deviation of the data and interpreted the results. The mean time taken by Becky to complete the event is 91.17 seconds, with a standard deviation of 3.51 seconds.

Future Work

In the future, we can use more advanced statistical techniques to analyze the data. For example, we can use regression analysis to model the relationship between the time taken and other variables, such as Becky's age or training experience.

References

• [1] Wikipedia. (2023). Time series. Retrieved from https://en.wikipedia.org/wiki/Time_series
• [2] Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice. OTexts.

Appendix

The data used in this article is available in the table below:

Introduction

In our previous article, we analyzed the time data of Becky's 100-meter freestyle event over the past six years. We calculated the mean, median, mode, and standard deviation of the data and interpreted the results. In this article, we will answer some frequently asked questions about the analysis.

Q: What is the purpose of analyzing time data?

A: The purpose of analyzing time data is to understand the trends and patterns in the data. In this case, we wanted to see how Becky's time in the 100-meter freestyle event changed over the past six years.

Q: What is the difference between the mean and median?

A: The mean is the average of all the observations, while the median is the middle value of the data when it is arranged in order. In this case, the mean is 91.17 seconds, while the median is 90 seconds.

Q: What is the mode, and why is it not present in this data?

A: The mode is the value that appears most frequently in the data. In this case, there is no mode, as each value appears only once.

Q: What is the standard deviation, and why is it important?

A: The standard deviation is a measure of the spread of the data. It is calculated as the square root of the variance. In this case, the standard deviation is 3.51 seconds, which means that the times are spread out over a range of 6.68 seconds (from 84.47 seconds to 98 seconds).

Q: How can we use regression analysis to model the relationship between the time taken and other variables?

A: We can use regression analysis to model the relationship between the time taken and other variables, such as Becky's age or training experience. This can help us understand how these variables affect the time taken and make predictions about future times.

Q: What are some limitations of this analysis?

A: Some limitations of this analysis include:

• The data is limited to six years, which may not be representative of Becky's overall performance.
• The data does not include other variables that may affect the time taken, such as weather conditions or course layout.
• The analysis assumes that the data is normally distributed, which may not be the case.

Q: How can we improve this analysis?

A: We can improve this analysis by:

• Collecting more data to increase the sample size and improve the accuracy of the results.
• Including other variables that may affect the time taken, such as weather conditions or course layout.
• Using more advanced statistical techniques, such as regression analysis, to model the relationship between the time taken and other variables.

Conclusion

In this article, we answered some frequently asked questions about analyzing time data. We discussed the purpose of analyzing time data, the difference between the mean and median, and the importance of the standard deviation. We also discussed how to use regression analysis to model the relationship between the time taken and other variables and some limitations of this analysis. We hope that this article has been helpful in understanding the analysis of time data.

References

• [1] Wikipedia. (2023). Time series. Retrieved from https://en.wikipedia.org/wiki/Time_series
• [2] Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice. OTexts.

Appendix

The data used in this article is available in the table below:

This data can be used to reproduce the results of this article.