The class with the greatest mean sales in a spring fundraiser will win a prize. The mean for Eric's class is $148. The mean for Natalia's class is $152. Natalia's sales total $150. If Natalia moves to Eric's class, the mean for each class increases. Explain why?
150 is less than the mean for Natalia's class. So, if that score is removed, the mean rises.
Similarly, since 150 is greater than the mean for Eric's class, if that score is added, the mean rises.
ya but it says both classes how does natillies class go up
No, it says the mean for EACH class increases 🤨🥴👉🏼👈🏼
I still don't understand but thanks anyways lol
Well, it seems that Natalia has really high sales! She's a fundraising queen! But, let's dive into the math behind this.
Currently, the mean for Eric's class is $148. That means, on average, each student in his class has sold $148 worth of stuff. But when we add Natalia's sales, which total $150, the overall mean for Eric's class would increase.
See, the mean is calculated by taking the sum of all the data points and dividing it by the total number of data points. Currently, we don't know the number of students in Eric's class. But let's assume there are "x" students.
So, the current mean for Eric's class is (148 * x + 150) / x.
Now, let's imagine Natalia moves to Eric's class. That means the new mean for Eric's class would be (148 * x + 150 + 152) / (x + 1). Why? Because there would be "x+1" students in the class.
Since 150 and 152 are both greater than 148, the numerator of the new mean equation is now larger, which leads to a larger overall mean. So, if Natalia moves to Eric's class, the mean for each class increases because those high sales of hers are having a positive impact on the average. Way to boost those stats, Natalia!
To understand why the mean for each class increases when Natalia moves to Eric's class, we need to look at the concept of mean and how it is calculated.
The mean, also known as the average, is calculated by summing all the values in a data set and then dividing it by the number of values.
In this case, we are comparing the mean sales for Eric's class and Natalia's class in a spring fundraiser. Let's break down the given information:
1. Eric's class:
- Mean sales: $148
2. Natalia's class:
- Mean sales: $152
- Natalia's sales total: $150
Now, let's consider what happens when Natalia moves from her own class to Eric's class:
- In Natalia's class:
- The total sales for Natalia's class remains the same ($150).
- The number of students in Natalia's class decreases by 1.
- Therefore, the mean sales in Natalia's class will remain the same ($152).
- In Eric's class:
- The total sales for Eric's class increases by $150 since Natalia brings her sales with her.
- The number of students in Eric's class increases by 1.
- Therefore, the mean sales in Eric's class will increase.
The increase in the total sales for Eric's class and the increase in the number of students will contribute to a higher mean sales value for Eric's class compared to Natalia's class.
Overall, when Natalia moves to Eric's class, both classes will experience an increase in their mean sales.