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## 6th grade (Eureka Math/EngageNY)

### Unit 6: Lesson 2

Topic B: Summarizing a distribution that is approximately symmetric using the mean and mean absolute deviation- Statistics intro: Mean, median, & mode
- Mean, median, & mode example
- Calculating the mean
- Calculating the mean
- Calculating the mean: data displays
- Missing value given the mean
- Mean as the balancing point
- Missing value given the mean
- Median & range puzzlers
- Median & range puzzlers
- Impact on median & mean: removing an outlier
- Impact on median & mean: increasing an outlier
- Effects of shifting, adding, & removing a data point
- Mean absolute deviation (MAD)
- Mean absolute deviation example
- Mean absolute deviation (MAD)

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# Impact on median & mean: increasing an outlier

AP.STATS:

UNC‑1 (EU)

, UNC‑1.K (LO)

, UNC‑1.K.2 (EK)

Sal thinks through the effects of modifying a value in a data set. What will happen to the mean and median?

## Want to join the conversation?

- I don't get the range, is it like average? Is it similar to the median? I'm really confused.(13 votes)
- The range is the max minus the min.

The average is the mean.

For example,

4, 3, 7, 9, 1, 5, 2

find the range and mean.

First, order the numerals in numerical order,

1, 2, 3, 4, 5, 7, 9

now first let's calculate the mean,

1+2+3+4+5+7+9 = 31

there are 7 numbers,

31 divided by 7 = 4.42857142857

now the range, easy.

what's 9 minus 1?

8.

range = 8

mean = 4.42857142857

(now that I think about it, this was a terrible example... it took like forever to calculate the mean...)(19 votes)

- For some reason I'm not seeing my comment in the comment section, so if it seems like I posted the same thing twice, I'm sorry.

I had a hard time understanding the wording with the first problem in this video because you didn't say "one number is literally 180, another is literally 220, and the 3rd number is somewhere in between those two." You said that the 3 other numbers (or high scores) are "[anywhere from] 180 to 220." Which means that they might**not**be 180 and 220; for example, the numbers could be 185, 192, and 216. So I think if you instead rewrote the problem like so: "Their scores are 180, 220, 250 and x" or something like that, learners would not have to guess what you are trying to say.(7 votes) - First, how did you conclude two of the values are 220 and 180, can't it also be something like 210 and 190 ?

Second, The median of even number is the mean of the two middle, why the mean of the two middles ? can't it be just a number between them, or it is just a convention(6 votes)- Probably the better way to state it would have been to say the 3 scores ranged from 180 to 220, ie 180, 220 and some unknown. Luckily, the actual values don't make any difference for this specific exercise. Only the change of the extreme value from 250 to 290 mattered.

Second, the statistical median determination in case of even number of data points is simply defined that way. I guess you could say were calculating the middle of the middle :)(4 votes)

- How can you take two of the numbers as 180 and 220 because the question only mentioned that the 3 scores were "
" 180 and 220?**between**(4 votes)- It's possible that the scores were just one less, which would make any calculations almost identical. Alongside that this question in particular isn't actually asking for any specific calculations, so it is easier to just use the numbers given rather than throwing more into the mix. This way you get the idea of what the distribution looks like.(2 votes)

- What is outlier?(2 votes)
- an outlier is a set of data far away from the other sets of data(5 votes)

- In class I’m not sure what a mean is the guy who is teaching us in the video I just don’t understand(2 votes)
- Keep on watching the video or ask questions that could help you and understand on what you are confused on.(0 votes)

- We're not told of their actual scores, but only a range, so Sal can't assume the 2 scores like he did.

Also, we don't know if the range is inclusive or not, so Sal especially can't assume that number can be 180 or 220.(2 votes) - how do find the original numbers with only knowing the mean and the amount of numbers(2 votes)
- Why did he onl say "that guy" why not "that girl"?(0 votes)
- That depends on his choice. He is a male. So I think he may choose it. I have seen ladies choose 'that girl' and men choose 'that guy'. I have seen my classmates too. It depends on your opinion.(4 votes)

- How did he figure out the median stayed the same and the mean increased(0 votes)
- The median is just the middle number (or the average of the 2 middle numbers if the set is even).

Since the high score increased, the average of all the numbers would increase. But since the middle 2 numbers stayed the same, the median would remain the same.

For instance, if the numbers were 1, 2, 3, 4, the average would be 1+2+3+4 divided by 4, or 2.5. The median would be the average of the middle 2 numbers. The average of 2 & 3, is 2+3 divided by 2, or 2.5.

If the numbers change to be 1, 2, 3, 10, the average would be 1+2+3+10 divided by 4, or 16/4, or 4. The median would still be the average of the 2 middle numbers, so 2 & 3, so would still be 2.5.

Good luck!(5 votes)

## Video transcript

- [Voiceover] Let's think about what happens to the median and mean of a set of numbers when I change one of the numbers. And so let's look at this example. A group of four friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game. Their high scores are all between 180 and 220, except for Adam, whose high score is 250. Adam then bowls a great game and has a new high score of 290. How will increasing Adam's high score affect the mean and median? Now, like always, pause this video and see if you can figure this out yourself. All right, so let's just think about what they're saying. We have four friends, and they each keep track of their all-time high score, so we're gonna have four data points, an all-time high score for each of the friends. So let's see, this is the lowest score of the friends, this is the second lowest, second to highest, and this is the highest scoring of the friends. So let's see. Their high scores are all between 100 and 220, except for Adam, whose high score is 250. So before Adam bowls this super-awesome game, the scores look something like this. The lowest score is 180. Adam scores 250. And if you take Adam out of the picture, the highest score is a 220. And we actually don't know what this score right over there is. Now, after Adam bowls a great new game and has a new high score of 290, what does the data set look like? Well, this guy's high score hasn't changed. This guy's high score hasn't changed. This guy's high score hasn't changed. But now Adam has a new high score. Instead of 250, it is now 290. So my question is, well, the first question is, does this change the median? Well, remember the median is the middle number. And if we're looking at four numbers here, the median is going to be the average of the middle two numbers. So we're gonna take the average of whatever this question mark is and 220. That's going to be the median. Now, over here, after Adam has scored a new high score, how do we calculate the median? Well, we still have four numbers, and the middle two are still the same two middle numbers. Whatever this friend's highest score was, it hasn't changed, and so we're gonna have the same median. It's gonna be 220 plus question mark, divided by two. It's gonna be halfway between question mark and 220. So our median won't change. So median, no change. Median, no change. So let's think about the mean now. Well, the mean, you take the sum of all these numbers and then you divide by four, and then you take the sum of all these numbers and divide by four. So which sum is going to be higher? Well, the first three numbers are the same, but in the second list you have a higher number. 290 is higher than 250. So if you take these four and divide by four, you're going to have a larger value than if you take these four and divide by four, because their sum is gonna be larger. And so the mean is going to go up. The mean will increase. The mean will increase. So median, no change, and mean, increase. All right, so this says both increase. No, that's not right. The median will increase. No, median doesn't change. The mean will increase. Yep. And the median will stay the same. Yep, that's exactly what we're talking about. And if you wanna make it a little bit more tangible, you can replace question mark with some number. You could replace it, maybe this question mark is 200. And if you try it out with 200, just to make things tangible, you're going to see that that is indeed going to be the case. The median would be halfway between these two numbers. And I just arbitrarily picked 200. It could be any number some place between 180 and 220, but you see, for this example, it's very tangibly that the median does not change. But the mean increases, 'cause we increase the sum. We increase the sum by 40, because we've increased this last number, and only the last number, by 40.