If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: AP®︎/College Statistics>Unit 4

Lesson 3: 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?
• Negative/left skew means that the data is mostly high values, so if you look at the graph, there's a long "tail" heading to the left. Positive/right skew means the opposite: lots of low values, long right tail.
• 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?
• I did not understand this sentence "Well the mean is, you take each of the possible values and you weight it by their frequencies, you weight it by their frequencies and you add all of that up". In particular the meaning of weighting in this context
• well, he is talking about
1)the possible values ie.
---the x axis intervals((0-1),(1-2) etc)

2)frequencies of data points in each given interval ie.
---the number of data points in that given interval.{Dont confuse it with y axis , as y axis in density curve will have relative frequency and not the no of data points. The number of data points info has to given to us}

If we get both of this information then,
-- all the data points values added and summed up
-- and then divided by the total no of data points.

Whatever the value comes, will be the mean, which can be marked on the graph at its interval.

EG IF MEAN =3.8
then it will be marked at in interval (3-4) with a strait line of density curve.

This is why SAL did that visually because he dodent have the no of data points.

Hope this helps.
(1 vote)
• @KhanAcademy, can you please do a video only based on skewed lines plz, thx😆😆😆
• what is an example of symmetrical distribution?
(1 vote)
• An extremely common example of a symmetrical distribution is the normal distribution (bell-shaped curve). So the mean and median of a normal distribution are the same. Since a normal distribution is also symmetric about its highest peak, the mode (as well as the mean and median) are all equal in a normal distribution.

Have a blessed, wonderful day!
• 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
• what do the different skews of data look like.
• he different skews of data can be visualized as follows:

Symmetric Distribution: In a symmetric distribution, the data is evenly distributed around the mean, with equal tails on both sides. The mean and median are equal, and the curve appears balanced.
Right Skewed (Positive Skew): In a right-skewed distribution, the tail of the curve extends towards higher values, creating a longer tail on the right side. The mean is greater than the median, and the curve appears to have a longer right tail.
Left Skewed (Negative Skew): In a left-skewed distribution, the tail of the curve extends towards lower values, creating a longer tail on the left side. The mean is less than the median, and the curve appears to have a longer left tail.
(1 vote)
• Why Balancing point become the mean? i can't understand it
• The mean is referred to as the balance point because assuming uniform density, if we were to put a fulcrum there, it would balance the "structure" out.
(1 vote)
• 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!