Find The Mean From A Frequency Table.The Frequency Table Below Summarizes A List Of The Weights (in Pounds) Of Orders Ready For Shipment At A Shoe Factory. Find The Mean.$\[ \begin{tabular}{|c|c|} \hline Value & Frequency \\ \hline 17 & 4
Introduction
In statistics, a frequency table is a table that displays the frequency of each value in a dataset. It is a useful tool for summarizing and analyzing large datasets. In this article, we will discuss how to find the mean from a frequency table. We will use a real-world example to illustrate the process.
Understanding the Frequency Table
A frequency table is a table that displays the frequency of each value in a dataset. It is typically organized into two columns: the first column lists the values, and the second column lists the frequency of each value. In our example, the frequency table below summarizes a list of the weights (in pounds) of orders ready for shipment at a shoe factory.
| Value | Frequency |
|---|---|
| 17 | 4 |
| 18 | 5 |
| 19 | 3 |
| 20 | 2 |
| 21 | 1 |
Step 1: Calculate the Total Frequency
The first step in finding the mean from a frequency table is to calculate the total frequency. This is the sum of all the frequencies in the table.
Total Frequency = 4 + 5 + 3 + 2 + 1 = 15
Step 2: Multiply Each Value by Its Frequency
The next step is to multiply each value by its frequency. This will give us the total weight for each value.
| Value | Frequency | Total Weight |
|---|---|---|
| 17 | 4 | 68 |
| 18 | 5 | 90 |
| 19 | 3 | 57 |
| 20 | 2 | 40 |
| 21 | 1 | 21 |
Step 3: Calculate the Total Weight
The next step is to calculate the total weight. This is the sum of all the total weights.
Total Weight = 68 + 90 + 57 + 40 + 21 = 276
Step 4: Calculate the Mean
The final step is to calculate the mean. This is the total weight divided by the total frequency.
Mean = Total Weight / Total Frequency = 276 / 15 = 18.4
Conclusion
In this article, we discussed how to find the mean from a frequency table. We used a real-world example to illustrate the process. By following these steps, you can easily find the mean from a frequency table.
Example Problems
Problem 1
Find the mean from the following frequency table:
| Value | Frequency |
|---|---|
| 25 | 3 |
| 26 | 4 |
| 27 | 2 |
| 28 | 1 |
Solution
Total Frequency = 3 + 4 + 2 + 1 = 10
| Value | Frequency | Total Weight |
|---|---|---|
| 25 | 3 | 75 |
| 26 | 4 | 104 |
| 27 | 2 | 54 |
| 28 | 1 | 28 |
Total Weight = 75 + 104 + 54 + 28 = 261
Mean = Total Weight / Total Frequency = 261 / 10 = 26.1
Problem 2
Find the mean from the following frequency table:
| Value | Frequency |
|---|---|
| 15 | 2 |
| 16 | 3 |
| 17 | 4 |
| 18 | 1 |
Solution
Total Frequency = 2 + 3 + 4 + 1 = 10
| Value | Frequency | Total Weight |
|---|---|---|
| 15 | 2 | 30 |
| 16 | 3 | 48 |
| 17 | 4 | 68 |
| 18 | 1 | 18 |
Total Weight = 30 + 48 + 68 + 18 = 164
Mean = Total Weight / Total Frequency = 164 / 10 = 16.4
Frequently Asked Questions
Q: What is a frequency table?
A: A frequency table is a table that displays the frequency of each value in a dataset.
Q: How do I calculate the mean from a frequency table?
A: To calculate the mean from a frequency table, you need to multiply each value by its frequency, calculate the total weight, and then divide the total weight by the total frequency.
Q: What is the total frequency?
A: The total frequency is the sum of all the frequencies in the table.
Q: What is the total weight?
A: The total weight is the sum of all the total weights.
Conclusion
Q: What is a frequency table?
A: A frequency table is a table that displays the frequency of each value in a dataset. It is a useful tool for summarizing and analyzing large datasets.
Q: How do I create a frequency table?
A: To create a frequency table, you need to list the values in one column and the frequency of each value in another column. For example:
| Value | Frequency |
|---|---|
| 17 | 4 |
| 18 | 5 |
| 19 | 3 |
| 20 | 2 |
| 21 | 1 |
Q: What is the total frequency?
A: The total frequency is the sum of all the frequencies in the table. For example, in the frequency table above, the total frequency is 4 + 5 + 3 + 2 + 1 = 15.
Q: How do I calculate the total weight?
A: To calculate the total weight, you need to multiply each value by its frequency. For example, in the frequency table above, the total weight is:
| Value | Frequency | Total Weight |
|---|---|---|
| 17 | 4 | 68 |
| 18 | 5 | 90 |
| 19 | 3 | 57 |
| 20 | 2 | 40 |
| 21 | 1 | 21 |
Total Weight = 68 + 90 + 57 + 40 + 21 = 276
Q: How do I calculate the mean?
A: To calculate the mean, you need to divide the total weight by the total frequency. For example, in the frequency table above, the mean is:
Mean = Total Weight / Total Frequency = 276 / 15 = 18.4
Q: What if I have a frequency table with missing values?
A: If you have a frequency table with missing values, you need to handle the missing values before calculating the mean. There are several ways to handle missing values, including:
- Ignoring the missing values and calculating the mean based on the remaining values
- Replacing the missing values with a specific value, such as the mean of the remaining values
- Using a more advanced method, such as imputation or interpolation
Q: What if I have a frequency table with outliers?
A: If you have a frequency table with outliers, you need to handle the outliers before calculating the mean. There are several ways to handle outliers, including:
- Ignoring the outliers and calculating the mean based on the remaining values
- Replacing the outliers with a specific value, such as the mean of the remaining values
- Using a more advanced method, such as robust regression or Winsorization
Q: Can I use a frequency table to calculate other statistics?
A: Yes, you can use a frequency table to calculate other statistics, such as the median, mode, and standard deviation. However, you need to follow the same steps as calculating the mean, including multiplying each value by its frequency, calculating the total weight, and then dividing the total weight by the total frequency.
Q: What are some common mistakes to avoid when working with frequency tables?
A: Some common mistakes to avoid when working with frequency tables include:
- Forgetting to multiply each value by its frequency
- Forgetting to calculate the total weight
- Forgetting to divide the total weight by the total frequency
- Ignoring missing values or outliers
- Using an incorrect method to handle missing values or outliers
Conclusion
In this article, we discussed frequently asked questions about finding the mean from a frequency table. We covered topics such as creating a frequency table, calculating the total frequency, calculating the total weight, and calculating the mean. We also discussed how to handle missing values and outliers, and how to use a frequency table to calculate other statistics. By following these steps and avoiding common mistakes, you can easily find the mean from a frequency table.