Charles Asked His Teammates How Many Hours They Practiced Swimming During The Week. He Recorded His Data In The Table Below And Used The Shaded Columns To Calculate Three Sample Means. What Is The Range Of The Values For The Sample
Introduction
In statistics, sample means are calculated by summing up the values of a dataset and dividing by the number of observations. The range of a dataset is the difference between the highest and lowest values. In this article, we will explore how to calculate sample means and ranges using a table of swimming practice hours.
Calculating Sample Means
Charles recorded the swimming practice hours of his teammates in the table below.
| Teammate | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 3 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
Charles used the shaded columns to calculate three sample means.
| Sample | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|---|
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| B | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| C | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
To calculate the sample mean for each column, we need to sum up the values and divide by the number of observations.
Calculating Sample Mean A
| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Sample Mean A = (2 + 3 + 4 + 5 + 6 + 7 + 8) / 7 = 35 / 7 = 5
Calculating Sample Mean B
| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Sample Mean B = (1 + 2 + 3 + 4 + 5 + 6 + 7) / 7 = 28 / 7 = 4
Calculating Sample Mean C
| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Sample Mean C = (3 + 4 + 5 + 6 + 7 + 8 + 9) / 7 = 42 / 7 = 6
Calculating Ranges
To calculate the range of the values for each sample, we need to find the difference between the highest and lowest values.
Range of Sample A
| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Highest Value = 8 Lowest Value = 2 Range = Highest Value - Lowest Value = 8 - 2 = 6
Range of Sample B
| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Highest Value = 7 Lowest Value = 1 Range = Highest Value - Lowest Value = 7 - 1 = 6
Range of Sample C
| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Highest Value = 9 Lowest Value = 3 Range = Highest Value - Lowest Value = 9 - 3 = 6
Conclusion
In this article, we calculated the sample means and ranges of three samples of swimming practice hours. We found that the sample means were 5, 4, and 6, and the ranges were 6, 6, and 6, respectively. This shows that the sample means and ranges can be used to describe the central tendency and variability of a dataset.
Key Takeaways
- Sample means are calculated by summing up the values of a dataset and dividing by the number of observations.
- Ranges are calculated by finding the difference between the highest and lowest values.
- Sample means and ranges can be used to describe the central tendency and variability of a dataset.
References
- [1] "Statistics for Dummies" by Deborah J. Rumsey
- [2] "Mathematics for Dummies" by Mary Jane Sterling
Frequently Asked Questions (FAQs) about Sample Means and Ranges ====================================================================
Q: What is a sample mean?
A: A sample mean is a statistical measure that represents the average value of a dataset. It is calculated by summing up the values of the dataset and dividing by the number of observations.
Q: How is a sample mean calculated?
A: To calculate a sample mean, you need to follow these steps:
- Sum up the values of the dataset.
- Count the number of observations in the dataset.
- Divide the sum of the values by the number of observations.
Q: What is a range?
A: A range is a statistical measure that represents the difference between the highest and lowest values in a dataset.
Q: How is a range calculated?
A: To calculate a range, you need to follow these steps:
- Identify the highest value in the dataset.
- Identify the lowest value in the dataset.
- Subtract the lowest value from the highest value.
Q: What is the difference between a sample mean and a range?
A: A sample mean represents the average value of a dataset, while a range represents the difference between the highest and lowest values in a dataset.
Q: Why are sample means and ranges important?
A: Sample means and ranges are important because they can be used to describe the central tendency and variability of a dataset. They can also be used to compare different datasets and make informed decisions.
Q: Can sample means and ranges be used to compare different datasets?
A: Yes, sample means and ranges can be used to compare different datasets. By comparing the sample means and ranges of different datasets, you can determine which dataset has the highest or lowest values, and which dataset has the most or least variability.
Q: What are some common applications of sample means and ranges?
A: Sample means and ranges have many common applications in various fields, including:
- Business: Sample means and ranges can be used to analyze customer satisfaction, employee productivity, and sales data.
- Medicine: Sample means and ranges can be used to analyze patient outcomes, treatment efficacy, and disease progression.
- Social Sciences: Sample means and ranges can be used to analyze demographic data, economic indicators, and social trends.
Q: How can I calculate sample means and ranges using a calculator or computer software?
A: There are many calculators and computer software programs that can be used to calculate sample means and ranges, including:
- Microsoft Excel
- Google Sheets
- SPSS
- R
Q: What are some common mistakes to avoid when calculating sample means and ranges?
A: Some common mistakes to avoid when calculating sample means and ranges include:
- Not checking for errors in data entry
- Not using the correct formula for calculating sample means and ranges
- Not considering outliers or missing data
- Not interpreting the results correctly
Conclusion
In this article, we have answered some frequently asked questions about sample means and ranges. We have discussed what sample means and ranges are, how they are calculated, and why they are important. We have also provided some common applications of sample means and ranges and some tips for avoiding common mistakes.