The Following Frequency Table Summarizes The Number Of Bicycles Sold On Saturdays During A 3-month Period. Estimate The Mean Of The Data Set Summarized In The Frequency Table. Round Your Answer To The Nearest
Understanding the Frequency Table
A frequency table is a table that displays the number of times each value in a dataset occurs. In this case, the frequency table summarizes the number of bicycles sold on Saturdays during a 3-month period. The table is as follows:
| Number of Bicycles Sold | Frequency |
|---|---|
| 0 | 2 |
| 1 | 3 |
| 2 | 5 |
| 3 | 4 |
| 4 | 2 |
| 5 | 1 |
Calculating the Mean
To estimate the mean of the data set, we need to calculate the midpoint of each interval and multiply it by the frequency of that interval. The midpoint of an interval is the average of the two endpoints of the interval.
Calculating the Midpoint of Each Interval
| Number of Bicycles Sold | Midpoint | Frequency |
|---|---|---|
| 0 | 0 | 2 |
| 1 | 0.5 | 3 |
| 2 | 1.5 | 5 |
| 3 | 2.5 | 4 |
| 4 | 3.5 | 2 |
| 5 | 4.5 | 1 |
Calculating the Product of Midpoint and Frequency
| Number of Bicycles Sold | Midpoint | Frequency | Product |
|---|---|---|---|
| 0 | 0 | 2 | 0 |
| 1 | 0.5 | 3 | 1.5 |
| 2 | 1.5 | 5 | 7.5 |
| 3 | 2.5 | 4 | 10 |
| 4 | 3.5 | 2 | 7 |
| 5 | 4.5 | 1 | 4.5 |
Calculating the Sum of Products
The sum of products is the sum of the products of midpoint and frequency.
Sum of products = 0 + 1.5 + 7.5 + 10 + 7 + 4.5 = 30
Calculating the Mean
The mean is the sum of products divided by the total frequency.
Total frequency = 2 + 3 + 5 + 4 + 2 + 1 = 17
Mean = Sum of products / Total frequency = 30 / 17 = 1.7647
Rounding the Mean to the Nearest Whole Number
The mean is approximately 1.7647. Rounding this to the nearest whole number gives us a mean of 2.
Conclusion
In this article, we estimated the mean of the data set summarized in the frequency table. We calculated the midpoint of each interval, multiplied it by the frequency of that interval, and then calculated the sum of products. Finally, we divided the sum of products by the total frequency to get the mean. We rounded the mean to the nearest whole number to get a final answer of 2.
References
- [1] "Frequency Tables." Wikipedia, Wikimedia Foundation, 12 Feb. 2023, en.wikipedia.org/wiki/Frequency_table.
- [2] "Mean." Wikipedia, Wikimedia Foundation, 12 Feb. 2023, en.wikipedia.org/wiki/Mean.
Further Reading
- [1] "How to Calculate the Mean of a Frequency Table." Math Is Fun, mathisfun.com/data/mean-frequency-table.html.
- [2] "Calculating the Mean of a Frequency Table." Khan Academy, khanacademy.org/math/statistics-probability/summarizing-quantitative-data/frequency-tables/v/calculating-the-mean-of-a-frequency-table.
Q: What is a frequency table?
A: A frequency table is a table that displays the number of times each value in a dataset occurs. It is a way to summarize and organize data, making it easier to analyze and understand.
Q: How do I calculate the mean of a frequency table?
A: To calculate the mean of a frequency table, you need to follow these steps:
- Calculate the midpoint of each interval.
- Multiply the midpoint by the frequency of that interval.
- Calculate the sum of products.
- Divide the sum of products by the total frequency.
Q: What is the midpoint of an interval?
A: The midpoint of an interval is the average of the two endpoints of the interval. For example, if the interval is 0-1, the midpoint is 0.5.
Q: How do I calculate the total frequency?
A: The total frequency is the sum of the frequencies of all the intervals. For example, if the frequency table is:
| Number of Bicycles Sold | Frequency |
|---|---|
| 0 | 2 |
| 1 | 3 |
| 2 | 5 |
| 3 | 4 |
| 4 | 2 |
| 5 | 1 |
The total frequency is 2 + 3 + 5 + 4 + 2 + 1 = 17.
Q: What is the difference between the mean and the median?
A: The mean is the average of all the values in a dataset, while the median is the middle value when the data is arranged in order. The mean is sensitive to outliers, while the median is more robust.
Q: How do I know if my frequency table is accurate?
A: To ensure the accuracy of your frequency table, you should:
- Double-check the data for errors.
- Verify that the frequencies are correct.
- Use a consistent method for calculating the midpoint and sum of products.
Q: Can I use a frequency table to estimate the mean of a large dataset?
A: Yes, you can use a frequency table to estimate the mean of a large dataset. However, you should be aware that the accuracy of the estimate may depend on the size of the dataset and the number of intervals.
Q: How do I interpret the results of a frequency table?
A: To interpret the results of a frequency table, you should:
- Look at the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the central tendency of the data.
Q: Can I use a frequency table to compare two or more datasets?
A: Yes, you can use a frequency table to compare two or more datasets. However, you should be aware that the accuracy of the comparison may depend on the size of the datasets and the number of intervals.
Q: How do I create a frequency table from a dataset?
A: To create a frequency table from a dataset, you should:
- Organize the data into intervals.
- Count the number of times each value occurs.
- Create a table with the intervals and frequencies.
Q: Can I use a frequency table to estimate the standard deviation of a dataset?
A: Yes, you can use a frequency table to estimate the standard deviation of a dataset. However, you should be aware that the accuracy of the estimate may depend on the size of the dataset and the number of intervals.
Q: How do I use a frequency table to make predictions about a dataset?
A: To use a frequency table to make predictions about a dataset, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to make predictions about the data.
Q: Can I use a frequency table to identify outliers in a dataset?
A: Yes, you can use a frequency table to identify outliers in a dataset. However, you should be aware that the accuracy of the identification may depend on the size of the dataset and the number of intervals.
Q: How do I use a frequency table to understand the skewness of a dataset?
A: To use a frequency table to understand the skewness of a dataset, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the skewness of the data.
Q: Can I use a frequency table to estimate the correlation between two datasets?
A: Yes, you can use a frequency table to estimate the correlation between two datasets. However, you should be aware that the accuracy of the estimate may depend on the size of the datasets and the number of intervals.
Q: How do I use a frequency table to understand the relationship between two variables?
A: To use a frequency table to understand the relationship between two variables, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the relationship between the variables.
Q: Can I use a frequency table to estimate the regression line of a dataset?
A: Yes, you can use a frequency table to estimate the regression line of a dataset. However, you should be aware that the accuracy of the estimate may depend on the size of the dataset and the number of intervals.
Q: How do I use a frequency table to understand the variance of a dataset?
A: To use a frequency table to understand the variance of a dataset, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the variance of the data.
Q: Can I use a frequency table to estimate the covariance between two datasets?
A: Yes, you can use a frequency table to estimate the covariance between two datasets. However, you should be aware that the accuracy of the estimate may depend on the size of the datasets and the number of intervals.
Q: How do I use a frequency table to understand the relationship between two variables in a multivariate dataset?
A: To use a frequency table to understand the relationship between two variables in a multivariate dataset, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the relationship between the variables.
Q: Can I use a frequency table to estimate the correlation matrix of a multivariate dataset?
A: Yes, you can use a frequency table to estimate the correlation matrix of a multivariate dataset. However, you should be aware that the accuracy of the estimate may depend on the size of the dataset and the number of intervals.
Q: How do I use a frequency table to understand the relationship between multiple variables in a multivariate dataset?
A: To use a frequency table to understand the relationship between multiple variables in a multivariate dataset, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the relationship between the variables.
Q: Can I use a frequency table to estimate the regression equation of a multivariate dataset?
A: Yes, you can use a frequency table to estimate the regression equation of a multivariate dataset. However, you should be aware that the accuracy of the estimate may depend on the size of the dataset and the number of intervals.
Q: How do I use a frequency table to understand the variance-covariance matrix of a multivariate dataset?
A: To use a frequency table to understand the variance-covariance matrix of a multivariate dataset, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the variance-covariance matrix of the data.
Q: Can I use a frequency table to estimate the correlation between multiple variables in a multivariate dataset?
A: Yes, you can use a frequency table to estimate the correlation between multiple variables in a multivariate dataset. However, you should be aware that the accuracy of the estimate may depend on the size of the dataset and the number of intervals.
Q: How do I use a frequency table to understand the relationship between multiple variables in a multivariate dataset with multiple outliers?
A: To use a frequency table to understand the relationship between multiple variables in a multivariate dataset with multiple outliers, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the relationship between the variables.
Q: Can I use a frequency table to estimate the regression equation of a multivariate dataset with multiple outliers?
A: Yes, you can use a frequency table to estimate the regression equation of a multivariate dataset with multiple outliers. However, you should be aware that the accuracy of the estimate may depend on the size of the dataset and the number of intervals.
Q: How do I use a frequency table to understand the variance-covariance matrix of a multivariate dataset with multiple outliers?
A: To use a frequency table to understand the variance-covariance matrix of a multivariate dataset with multiple outliers, you should:
- Analyze the distribution of the data.
- Identify any patterns or trends.
- Use the mean and median to understand the variance-covariance matrix of the data.
Q: Can I use a frequency table to estimate the correlation between multiple variables in a multivariate dataset with multiple outliers?
A: Yes, you can use a frequency table to estimate the correlation between multiple variables in a multivariate dataset with multiple outliers. However, you should be aware that the accuracy of the estimate may depend on the size of the dataset and the number of intervals.