Analyzing the Calculations

Oct 13, 2025 by miodeya.com 118 views

Introduction

In mathematics, the mean of a data set is a fundamental concept used to describe the central tendency of a set of numbers. It is calculated by summing up all the values in the data set and then dividing by the total number of values. In this article, we will analyze the work of four students, Ashrita, Collette, Ryan, and Emily, who attempted to find the mean of the data set ${ $26, 31, 39, 30, 16, 16, 18, 38\$}$ . Our goal is to determine which student found the correct mean.

Ashrita's Work

Ashrita's work is as follows:

${ \frac{26 + 31 + 39 + 30 + 16 + 16 + 18 + 38}{8} = \frac{214}{8} = 26.75 }$

At first glance, Ashrita's work appears to be correct. However, let's take a closer look at the calculation.

Step 1: Summing up the values

The first step in calculating the mean is to sum up all the values in the data set.

${ 26 + 31 + 39 + 30 + 16 + 16 + 18 + 38 = 214 }$

Step 2: Dividing by the total number of values

The next step is to divide the sum by the total number of values, which is 8 in this case.

${ \frac{214}{8} = 26.75 }$

Collette's Work

Collette's work is not provided in the problem statement. However, we can assume that she may have made a different calculation.

Ryan's Work

Ryan's work is not provided in the problem statement. However, we can assume that he may have made a different calculation.

Emily's Work

Emily's work is not provided in the problem statement. However, we can assume that she may have made a different calculation.

Analyzing the Calculations

Let's analyze the calculations made by each student.

Ashrita's calculation appears to be correct at first glance. However, we need to verify if the calculation is correct.
Collette's, Ryan's, and Emily's calculations are not provided, so we cannot analyze them.

Verifying Ashrita's Calculation

To verify Ashrita's calculation, we need to check if the calculation is correct.

${ \frac{26 + 31 + 39 + 30 + 16 + 16 + 18 + 38}{8} = \frac{214}{8} = 26.75 }$

However, let's recheck the calculation.

${ 26 + 31 + 39 + 30 + 16 + 16 + 18 + 38 = 214 }$

This is correct. However, let's recheck the division.

${ \frac{214}{8} = 26.75 }$

This is also correct. Therefore, Ashrita's calculation is correct.

Conclusion

In conclusion, Ashrita's calculation is correct. The mean of the data set ${ $26, 31, 39, 30, 16, 16, 18, 38\$}$ is indeed 26.75.

Key Takeaways

The mean of a data set is calculated by summing up all the values and then dividing by the total number of values.
Ashrita's calculation is correct.
Collette's, Ryan's, and Emily's calculations are not provided, so we cannot analyze them.

Final Answer

Q&A: Calculating the Mean

Q: What is the mean of a data set?

A: The mean of a data set is a fundamental concept used to describe the central tendency of a set of numbers. It is calculated by summing up all the values in the data set and then dividing by the total number of values.

Q: How do I calculate the mean of a data set?

A: To calculate the mean of a data set, follow these steps:

Sum up all the values in the data set.
Count the total number of values in the data set.
Divide the sum by the total number of values.

Q: What is the formula for calculating the mean?

A: The formula for calculating the mean is:

${ \text{Mean} = \frac{\text{Sum of values}}{\text{Total number of values}} }$

Q: How do I verify if my calculation is correct?

A: To verify if your calculation is correct, follow these steps:

Check if the sum of the values is correct.
Check if the total number of values is correct.
Check if the division is correct.

Q: What if I make a mistake in my calculation?

A: If you make a mistake in your calculation, you will get an incorrect answer. To avoid this, make sure to double-check your work and verify your calculation.

Q: Can I use a calculator to calculate the mean?

A: Yes, you can use a calculator to calculate the mean. However, make sure to double-check your work and verify your calculation to ensure accuracy.

Q: What if I have a large data set?

A: If you have a large data set, you can use a calculator or a computer program to calculate the mean. However, make sure to double-check your work and verify your calculation to ensure accuracy.

Q: Can I use a formula to calculate the mean?

A: Yes, you can use a formula to calculate the mean. The formula is:

${ \text{Mean} = \frac{\text{Sum of values}}{\text{Total number of values}} }$

Q: What is the importance of calculating the mean?

A: Calculating the mean is important because it helps to describe the central tendency of a data set. It is used in various fields such as statistics, economics, and business to make informed decisions.

Q: Can I use the mean to compare two or more data sets?

A: Yes, you can use the mean to compare two or more data sets. However, make sure to consider other factors such as the standard deviation and the range to get a more accurate comparison.

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

A: The mean and the median are both measures of central tendency. However, the mean is sensitive to extreme values, while the median is not. The median is the middle value of a data set when it is arranged in order.

Q: Can I use the mean to predict future values?

A: Yes, you can use the mean to predict future values. However, make sure to consider other factors such as the trend and the seasonality to get a more accurate prediction.

Conclusion

In conclusion, calculating the mean is an important concept in mathematics and statistics. It is used to describe the central tendency of a data set and is used in various fields such as statistics, economics, and business to make informed decisions. By following the steps outlined in this article, you can calculate the mean of a data set and use it to make informed decisions.

Key Takeaways

The mean of a data set is a fundamental concept used to describe the central tendency of a set of numbers.
The mean is calculated by summing up all the values in the data set and then dividing by the total number of values.
The formula for calculating the mean is:

${ \text{Mean} = \frac{\text{Sum of values}}{\text{Total number of values}} }$

You can use a calculator or a computer program to calculate the mean.
The mean is used in various fields such as statistics, economics, and business to make informed decisions.

Final Answer

The final answer is 26.75.