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### Course: Algebra 2 (Eureka Math/EngageNY)>Unit 4

Lesson 4: Topic B: Lesson 8: Distributions—Center, shape, and spread

# Means and medians of different distributions

Sal compares the mean and median based on a few different distributions. Created by Sal Khan.

## Want to join the conversation?

• I dont understand : in the following exercises "Interpreting and comparing data distributions", the questions are about standard deviation, but Sal haven t mentioned it yet.
• Why are there in the exercise right after this video questions about interquartile range and greatest deviations? I don't even know what these notions mean
• They misplaced the exercise, it happens from time to time... Next sections cover those topics.
• If the population is college graduates, Michael Jordan shouldn't have been included (he turned pro before graduating)
• The question is specifically asking about the median income of "geology majors" not "graduates of UNC with a degree in geology".
• Doesn't an outlier affect the median somewhat because it is a number used to locate the median correct.. The way this is worded it seems like the outliers don't affect the median, only the mean.... am I understanding this correctly
• Outliers do affect the median, for the reason you say. However, there needs to be many (relative to the size of the dataset) extreme values before the median gets changed.

Say we have a dataset: 1, 2, 3, 4, 5
The median is 3. If we changed the 5 to 500, the median will still be 3 (but the mean will not be!). If we changed the 4 and 5 to 400 and 500, the median would still be 3.

So for the median, it's not so much the size of the outlier, but rather how many there are. For the mean, even a single outlier can have a big effect if it is extreme enough.
• (scratches head) where did he get the data?
• You recorded the time in seconds it took for 8 participants to solve a puzzle. These times appear below. However, when the data was entered into the statistical program, the score that was supposed to be 22.1 was entered as 21.2. You had calculated the following measures of central tendency: the mean, the median, and the mean trimmed 25%. Which of these measures of central tendency will change when you correct the recording error?
• It depends on the position of the data value. If it is in the "middle", then the median will change, but otherwise it would remain the same. Likewise, the mean trimmed 25% would only change if the incorrectly entered value was not a truncated / trimmed one. The mean would change.
• What's mean and what's median?
• The mean is the average of all the numbers [sum of all numbers / the amount of numbers in the set] while the median is the middle number in a set that is arranged from smallest to largest. For example, you have

2, 3, 5, 6, 7, 8, 9,

The mean would be 2 + 3 + 5 + 6 + 7 + 8 + 9 / 7 = 32.3, while the median would be 6 because it is the middle number.

If the amount of numbers in the sequence is even, take the mean of the middle two numbers. For example, you have

2, 5, 6, 7, 8, 9

The median would be 7 + 6 / 2 = 6.5

Hope this helps!😀
• I need a quick refresher, what is a median again?
• If you organise all of the data in a data set in ascending or descending order, you will have two cases:
Odd number of data points: the middle value will be your median
Even number of data points: You have to take the average of your two middle terms to find the median
• what is a standard deviation?
• Standard Deviation is the measure of how far a typical value in the set is from the average. The smaller the Standard Deviation, the closely grouped the data point are. The standard deviation of {1,2,3} would be less than the Standard Deviation of {0,4,7,10}