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Lesson 5: Mean and median challenge problems

# Impact on median & mean: removing an outlier

In this golf game, Ana's lowest score of 80 was removed due to rule-breaking. This change increased both the mean and median of her remaining scores. However, the mean increased more than the median.

## Want to join the conversation?

• Won't removing an outlier be manipulating the data set? This video shows how the mean and median can change when the outlier is removed. So, if a scientist does some tests and gets an outlier, he/she can remove it to change the results to what he/she wants. So, I ask again, won't removing an outlier be unfairly changing the results? •  Depends. You're right that a scientist can't just arbitrarily discard a result, but if she'd been getting consistent results previously an outlier would suggest some kind of experimental error. If she can identify the source of that error then she is justified in removing the data.
In the video, it turned out that the score of 80 was as a result of "cheating", so we are right to discount it.
• I remember much about mean, but not so much about the rest. can someone fill me in? • Mean: Add all the numbers together and divide the sum by the number of data points in the data set.
Example: Data set; 1, 2, 2, 9, 8. (1 + 2 + 2 + 9 + 8) / 5

Median: Arrange all the data points from small to large and choose the number that is physically in the middle. If there is an even number of data points, then choose the two numbers in the (physical) middle and find the mean of the two numbers.
Example: Data set; 1, 2, 2, 9, 8, 10. Small to Large; 1, 2, 2, 8, 9, 10. Find the mean of 2 & 8.

Mode: The mode is the number that appears most frequently in a data set.
Example: Data set; 1, 2, 2, 9, 4, 10, 4. Mode: 2 and 4
• Bro who is here in 2023 • Why is Ana so bad at golf • At . If removing a number that is larger than the mean will make the mean itself go down, what will then happen with the median in this case? (when removing a number larger than the median) • Pretty useful but how will we solve for the mean if it has a negative number? • Starting from to , how does Sal find the mean without calculating? I thought about it and still couldn't understand how the mean increases, because removing one number means decreasing the total. If he removed 80, the original mean would drop. • Ana is really really BAD at golf 🤨 • Today I will define this: ➗. A division symbol. You use division to find how many parts go into the whole.
It looks like a dot above a line, above a dot.
Thanks!😁 • at ,why does the mean have to go up?
(1 vote) • 80 is the lowest score.
All the other four scores are greater than 80, so they can be written as
80 + 𝑎, 80 + 𝑏, 80 + 𝑐, and 80 + 𝑑, for some positive values 𝑎, 𝑏, 𝑐, 𝑑.

The mean of these five scores is
(80 + (80 + 𝑎) + (80 + 𝑏) + (80 + 𝑐) + (80 + 𝑑))∕5 =
= (5 ∙ 80 + 𝑎 + 𝑏 + 𝑐 + 𝑑)∕5 = 80 + (𝑎 + 𝑏 + 𝑐 + 𝑑)∕5

If we remove the lowest score, then the new mean will be
((80 + 𝑎) + (80 + 𝑏) + (80 + 𝑐) + (80 + 𝑑))∕4 =
= (4 ∙ 80 + 𝑎 + 𝑏 + 𝑐 + 𝑑)∕4 = 80 + (𝑎 + 𝑏 + 𝑐 + 𝑑)∕4

𝑎, 𝑏, 𝑐, 𝑑 > 0 ⇒ 𝑎 + 𝑏 + 𝑐 + 𝑑 > 0 ⇒
⇒ (𝑎 + 𝑏 + 𝑐 + 𝑑)∕4 > (𝑎 + 𝑏 + 𝑐 + 𝑑)∕5, and thereby the new mean must be greater than the previous mean.