the class with greatest mean.will win prize. the.mean of eric class of 148$. the mean of natalia class is $ 152 .natalia sales total is $150.if natalia moves to.eric class mean.of both classes increases... explain how
natalia's sales total is below the mean for her class
... so if she moves to another class, the mean for her original class will increase
natalia's sales total is above the mean for eric's class
... so if she moves to eric's class, the mean for the class will increase
To explain how the mean of both classes increases when Natalia moves to Eric's class, we need to consider the given information.
Given:
- The mean of Eric's class is $148.
- The mean of Natalia's class is $152.
- Natalia's sales total is $150.
To find out how the mean of both classes would increase if Natalia moves to Eric's class, we need to calculate the new mean for both classes.
Currently, the mean of Eric's class is $148. Since there is no further information given about Eric's class, we cannot determine the exact number of students or the new mean after Natalia joins.
However, we do have additional information about Natalia's class. We know that the mean of Natalia's class is $152 and her sales total is $150. From this information, we can calculate the total sum of all the sales made by Natalia's classmates.
Let's assume there are 'n' students in Natalia's class, excluding Natalia herself. So, the sum of sales made by Natalia's classmates would be $150 x n.
Now, if Natalia moves to Eric's class, the new mean of Eric's class would increase. This means the total sum of sales made by Natalia's classmates would also likely increase.
Here's the step-by-step process to calculate the new mean:
1. Calculate the sum of sales made by Natalia's classmates in her current class: $150 x n.
2. Calculate the new sum of sales made by Natalia's classmates if she moves to Eric's class: ($150 x n) + $150.
3. We don't have enough information to calculate the new mean of Eric's class because we need to know the number of students in that class.
Therefore, we can conclude that if Natalia moves to Eric's class and the mean of both classes increases, it would be because the total sum of sales made by Natalia's classmates in Eric's class would likely be higher than in her current class.
To determine how moving Natalia to Eric's class affects the mean of both classes, here's how we can calculate it step by step:
1. Find the sum of Eric's class: Since the mean of Eric's class is $148, we need to find the total sum of the class. Let's say there are n students in Eric's class. The sum of Eric's class is then n * 148.
2. Find the sum of Natalia's class: Since the mean of Natalia's class is $152, and her sales total is $150, we can calculate the number of students in Natalia's class by dividing her sales total by the mean. So, the number of students in Natalia's class is 150 / 152 ≈ 0.98 (rounded to the nearest whole number). We'll assume there is 1 student in Natalia's class.
3. Calculate the new mean of both classes: When Natalia moves to Eric's class, the sum of both classes will be Eric's sum (n * 148) plus Natalia's sum ($150). The new total number of students will be n + 1 (Eric's class students plus Natalia). Therefore, the new mean will be (n * 148 + 150) / (n + 1).
4. Compare the mean before and after Natalia's move: To determine if the mean increases or decreases when Natalia moves to Eric's class, we can compare the two mean values.
- If the new mean is greater than the mean of Eric's class (148), it means that the mean of both classes increases after Natalia's move.
- If the new mean is equal to the mean of Eric's class (148), it means that the mean remains the same after Natalia's move.
- If the new mean is less than the mean of Eric's class (148), it means that the mean decreases after Natalia's move.
By following these steps, you can determine how moving Natalia to Eric's class affects the mean of both classes.