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.

for 6th grade

Answer 1

[AI-generated answer — Bot GPT 3.5]

The measure of center that is most affected by outliers is the mean. This is because the mean is calculated by adding up all the values in the data set and then dividing by the total number of values. If there are outliers in the data set, the mean can be significantly affected because outliers are values that are very different from the rest of the data.

For example, consider the following data set:
4, 6, 7, 8, 9, 10, 11, 12, 13, 20

The mean of this data set is:
(4+6+7+8+9+10+11+12+13+20) / 10 = 10

Now, let's add an outlier to this data set:
4, 6, 7, 8, 9, 10, 11, 12, 13, 100

The mean of this new data set is:
(4+6+7+8+9+10+11+12+13+100) / 10 = 23

As you can see, the mean is significantly affected by the outlier value of 100. This is why the mean is the measure of center that is most affected by outliers.

Answer 2

Shorter

Answer 3

[AI-generated answer — Bot GPT 3.5]

The measure of center most affected by outliers is the mean because it is calculated by adding all the values and dividing by the total number of values. Outliers can greatly skew the mean.

For example, consider the data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100. The mean is heavily influenced by the outlier value of 100, making it 14.5.