The measure of center that is most affected by outliers is the mean.
The mean is calculated by summing up all of the data points and dividing the sum by the number of data points. Because the mean takes into account the specific values of each data point, it is heavily influenced by extreme values or outliers.
For example, consider the following data set:
10, 12, 15, 18, 20, 22, 24, 26, 28, 100
The mean of this data set is (10+12+15+18+20+22+24+26+28+100)/10 = 25.5.
However, the outlier value of 100 greatly affects the mean, pulling it higher than the majority of the data points. In this case, the mean is not a good representation of the central tendency of the data set due to the presence of the outlier.
In contrast, the median and mode are less affected by outliers. The median is the middle value of a data set when it is ordered, and the mode is the value that appears most frequently. Since the median and mode only consider the order or frequency of data points, they are not greatly impacted by extreme values.
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......
7 answers
Make it sound like a 5th grader wrote it but still give the answer and explain
The middle number in a set of numbers is called the mean. Outliers are numbers that are super big or super small compared to the other numbers. The mean gets all crazy and changes a lot if there are outliers. For example, if we have these numbers: 10, 12, 15, 18, 20, 22, 24, 26, 28, 100, the mean would be 25.5 because that super big 100 messes it up.
But the median and mode don't care about those crazy outliers. The median is just the number in the middle, and the mode is the one that shows up the most. They don't get messed up by big or small numbers like the mean does. So, the mean is the one that gets really changed by outliers.
But the median and mode don't care about those crazy outliers. The median is just the number in the middle, and the mode is the one that shows up the most. They don't get messed up by big or small numbers like the mean does. So, the mean is the one that gets really changed by outliers.
make it smaller
The mean is the middle number in a set of numbers. Outliers, like super big or small numbers, can make the mean go all crazy! But the median and mode don't care about outliers and stay the same. So, the mean is the one that gets really changed by outliers.
still expalin
Sure, I can explain with fewer words:
The mean is the middle number in a list. Outliers, like super big or small numbers, can make the mean go all crazy! But the median and mode don't care about outliers and stay the same. So, the mean is most affected by outliers.
The mean is the middle number in a list. Outliers, like super big or small numbers, can make the mean go all crazy! But the median and mode don't care about outliers and stay the same. So, the mean is most affected by outliers.