Question

Question Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points. ( make it like a 6th grader wrote it)

Answer 1

[AI-generated answer — Bot GPT 3.5]

Out of mean, median, and mode, the measure of center most affected by outliers is the mean. That's because the mean is calculated by adding up all the numbers and dividing by how many there are. Outliers, which are numbers that are much higher or lower than the others, can really change the total when you add them in.

For example, let's say we have these 10 numbers: 2, 3, 4, 5, 6, 7, 8, 9, 20, and 30. The mean of these numbers is (2+3+4+5+6+7+8+9+20+30) / 10 = 94 / 10 = 9.4. But if we add an outlier, like 100, the mean becomes (2+3+4+5+6+7+8+9+20+30+100) / 11 = 194 / 11 = 17.6. The mean changed a lot because of the outlier 100.

On the other hand, the median is not much affected by outliers. The median is the middle number when the numbers are listed in order. In our example, the median is still 7 even if we add the outlier 100. The mode, which is the number that appears the most, can also stay the same even with outliers. In our example, the mode is still 2 and 3 even when we add the outlier 100. So, the mean is the one most affected by outliers.

Answer 2

make it shorter

Answer 3

[AI-generated answer — Bot GPT 3.5]

Out of mean, median, and mode, the measure of center most affected by outliers is the mean. This is because the mean is calculated by adding up all the numbers and dividing by how many there are. Outliers, which are numbers that are much higher or lower than the others, can really change the total when you add them in.

For example, if we have these 10 numbers: 2, 3, 4, 5, 6, 7, 8, 9, 20, and 30, the mean is 9.4. But if we add an outlier like 100, the mean becomes 17.6. The median, which is the middle number when numbers are listed in order, and the mode, which is the number that appears the most, are not much affected by outliers. Therefore, the mean is the measure of center most easily changed by outliers.

Answer 4

shorter

Answer 5

[AI-generated answer — Bot GPT 3.5]

Outliers affect the mean the most because it is calculated by adding up all the numbers and dividing by how many there are. For example, in a set of 10 numbers, adding an outlier can cause the mean to change significantly. The median and mode are less affected by outliers.