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## Statistics and probability

### Course: Statistics and probability>Unit 4

Lesson 4: Density curves

# Median, mean and skew from density curves

High level analysis of density curves. A focus on median, mean, left-skew and right-skew.

## Want to join the conversation?

• I've heard of terms such as Positively and Negatively Skewed and that's why I watched this video. Can anyone explain what those terms mean? • Thank you for your great channel! I am puzlled by your definition of mean and median here because essentially they are the same you mentioned:

Median is the point where the area under the density curve to the left is equal to the area to the right. That is the same meaning for the point representing the mean as when you multiply each point by its probability you get the area under and the balancing point is the point in which areas on both sides balance each other! so for the left-skewed and right-skewed I do not understand how you differentiate between median and mean to be different! • It's true that we can view the mean as the balancing point, but that does not imply that the area to the left of the mean is equal to the area to the right.

For example, suppose that Archie weighs significantly more than Betty.
Then, with Archie on one end of a seesaw and Betty on the other end, the balancing point will definitely be closer to Archie but not directly underneath him!

The center of mass ("median") is not necessarily the same as the center of momentum ("mean").
• at , why we can use the physical method to find the mean? • what is an example of symmetrical distribution?
(1 vote) • hi how you doing, one question didn't you say that median is the best for getting the central tendency of data but in getting the median from the density curve in the median mislead us in getting the central tendency so when to use media as a way to get the central tendency thank :D • @KhanAcademy, can you please do a video only based on skewed lines plz, thx😆😆😆 • so, does this mean that the MEDIAN has 50%(area on the left) on it's left side and 50%(area on the right) on it's right side?
(1 vote) • Yes. The last two graphs can seem confusing, since they aren't symmetrical distributions. Try to imagine the graph as a plank with rocks of increasingly heavier weight, the heaviest ones on one side and the lightest ones on the other. The median is a fulcrum you can put under the plank. Where could you put the fulcrum so that the weight on both sides of the plank would be equal?

In this instance, you would put the fulcrum (median) closer to the heavier rocks, so that there would be enough of the lighter rocks to compensate for the weight difference.

Hope this helps!
• what can you say of the skewness in each of the following cases?
Mode=32.1 and Mean=35.4
median=1459 and Mean=1403
Median=50 and Mode=50
(1 vote) • Problem 1: I believe that the mode would be the highest peak in the density graph, since it is the most common number. Since the mean is larger than it (and hence to the "right"), the graph should be right-skewed.

Problem 2: The graph would be left-skewed since the mean is smaller than the median and hence to the "left".

Problem 3: Using similar logic as problem 1, the mode is the peak of the density curve. Since the median is the "middle number" and it's equal to the mode, the mode would also be in the middle of the graph. I believe this would result in a symmetric curve.

Hope this helps!😄
(1 vote)
• How to find equal value? Time-
(1 vote) • Although I understand the general ideas after watching this video, just to make sure I understand and can use the terms correctly, what does frequency mean when talking about density curves? Frequency is mentioned at around the mark just for reference. Thank you to anyone who is able to help! :)
(1 vote) 