Part C
Two days later, Kelly surveyed the same 13 classmates and found that none of them had been given math homework since she last surveyed them.
By how much does the mean of Kelly’s second data set change in comparison with the mean of the data set in her original survey? Explain how to determine the change in the means without calculating the mean of either data set.
What is the answer
To determine the change in the means without calculating the mean of either data set, you can use the following steps:
1. Recall that the mean is the average of a set of numbers. In this case, the mean represents the average amount of math homework given to the classmates.
2. Consider the first data set from the original survey. Since every classmate was given math homework, the mean value will be greater than zero.
3. In the second data set, none of the classmates were given math homework. This means that the average amount of math homework given in the second data set is zero.
4. The change in the means can be determined by finding the difference between the mean of the second data set and the mean of the original data set.
5. Since the mean of the original data set is greater than zero and the mean of the second data set is zero, the change in the means will be equal to the mean of the original data set.
In other words, the mean of the second data set is reduced to zero from the original mean value. Therefore, the change in the means is equal to the mean of the original data set.
To determine the change in the means without calculating the mean of either data set, you can use the concept of "averages balance."
The mean of a set of numbers represents the balance point or the center of the data. If we imagine a see-saw with data points on one side and the mean on the other, the mean would be the point at which the see-saw is perfectly balanced.
In this case, Kelly surveyed the same 13 classmates twice. In the first survey, the students had some math homework, and in the second survey, they had no math homework. Since none of the classmates had been given math homework in the second survey, the data points that represented the homework in the first survey are now missing.
Now, consider the see-saw analogy. The missing data points in the second survey can be thought of as the counterbalance to the homework data points in the first survey.
As a result, the overall balance or center of the data would shift towards the side without homework. This shift in balance reflects the difference in means between the two data sets.
Therefore, without calculating the means, we can conclude that the mean of Kelly's second data set would be lower than the mean of the original survey because the missing homework data points in the second survey would shift the balance towards a lower average.