Descriptive Statistics: The median
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- เผยแพร่เมื่อ 1 ส.ค. 2024
- See all my videos at www.zstatistics.com/videos/
0:00 Introduction
1:02 Definition
4:48 Mean vs Median
8:52 Challenge Question
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I would say this is especially relevant when looking at salaries. The average (mean) salary in a country could increase significantly if only the few top earners had their salaries increased. However, the median would barely change at all. Makes a big difference when politicians or economists refer to "average salaries" increasing, as it could mean almost nothing for those not in the top high-earning brackets.
That makes perfect sense to me.
@@anirudhranjan2934 It definitely does...
Spot on!
while choosing a college, looking at their median package offered in placements would give a better picture than mean package offered
And yet all the college's marketing/advertising campaign seems to care about is the highest package (not even the mean).
@@abishekraju4521 lmao
This is amazing. Simply amazing. I have no words to describe how intuitive you made statistics for me. You have a gift of simplifying things to great detail and the ability to do justice to teaching this subject. I've only rarely come across such great teachers and every time their skillfulness amazes me. Thanks a lot.
I agree I am studying psychology online, and the university material was not good enough for me to understand. Now I am watching your videos, and everything makes sense. Will show the uni your channel so they have an example to follow!
In calculating per capita income, instead of mean , median would be a good measure in order to determine country's earning capability.
Another scenario would be the time taken for the Newcastle to Sydney train to arrive at Central Station. The median time would be around 5 minutes after the scheduled time while the average time would be closer to 10 minutes after the scheduled time when factoring in all the delays.
Salaries and Car prices were the first things that came to my mind.
Any scenario which is the case of positional average.
Great explanation here! I’d say household income is right skewed.
Median would be preferable in describing measurements of elapsed time, e.g. how long to walk a mile. More generally, when there is a hard limit on one end of the distribution (zero on elapsed time), the median is usually more indicative.
Monthly tuition fees charged by different schools for a particular grade in a district. Do you think median is appropriate here?
Prices of different finished good (irrespective of the different categories, however, in some cases within the same category also there is significant variation)
Median - removing outliers (clouds and bad pixels) in satellite imagery temporal collections (scenes) over a region.
GDP of different countries located in the different political-economics area
Bank investment rate
Thank you so much for doing this! I've just subscribed to your channel :)
Median would be prefered for finding the central score among a class of students where some high scholar or less scholar students might skew the data. Plz correct me if I am wrong. 🙂
median for stock price over long periods?
I think the median will be a great choice in any skewed data . For Example salary distribution, Students grades , ETC . Consequently *any skewed data is a good example*
The average speed, or harmonic mean, of Roshan's morning cycle can be calculated as follows:
First, calculate the total distance traveled in each stage:
Stage 1:
Climb: 10 km/h * 0.5 hours = 5 km
Descent: 50 km/h * 0.5 hours = 25 km
Total: 5 km + 25 km = 30 km
Stage 2:
Flat cycle: 40 km/h * 0.5 hours = 20 km
Next, calculate the total time spent in each stage:
Stage 1: 0.5 hours
Stage 2: 0.5 hours
Total: 0.5 hours + 0.5 hours = 1 hour
Finally, calculate the harmonic mean of the average speed:
Harmonic Mean: Total distance / Total time = (30 km + 20 km) / 1 hour = 50 km/h
So, Roshan's average speed is 50 km/h.
I think a good example would be when calculating the average IQ of a population sample. One high IQ might increase the mean, meanwhile the median would be representing more "fairly" let's say.
Anyway, THANK YOU!!! I wish every teacher on the planet would apply your method.
salaries?
avg speed= 20.68km/hr. Is the answer correct?
what will be the best for this ? 1,2,3,100,400,1000 ?
is it mean or median?
(Caveat: I am NOT an expert!). Your set seems left (or negatively) skewed. The total is 1506. The average (mean) would be302, which is not really representative of the set overall. The median (103/2 = 56.5) seems even less representative. Neither choice is optimal, but - gun to the head option - I'd choose the mean.
@@m.c.degroffdavis9885 The Mean (Average) is 251 (=1506/6) and NOT 302 (~1506/5). You are right that neither is perfect; however, I'd choose the Median since, I think, it better reflects the "center" of data.
Plss someone tell me what's the use of sorting the data in ascending order to get median
For finding the median, it doesn't matter whether the data is sorted in ascending or descending order. Both directions will work. Ascending is just more intuitive.
@@skaniol first of all, thnx buddy to reply me 😇 it means a lot. But I have a very foolish doubt that" the data needs to be sorted in either of the two? "
@Mukesh Joshi The numbers in a statistical dataset could be enumerated or stored in any order. A dataset like (3,4,6,2,3) contains the same data as (2,3,3,4,6), but in a different order, so they aren't exactly equivalent, although you can easily turn the 1st one into the 2nd by sorting.
The order may matter or not, depending on what you are doing with the data. If you are calculating the mean, then it doesn't matter, but if you are calculating the median-the order is extremely important.
Why? The median would be meaningless if the data isn't sorted. Any one number from the dataset could happen to be positioned at the middle when we measure it. A random number there doesn't tell us anything about the other numbers. In the example above, the middle number happens to be 6 in the 1st dataset, while it's 3 in the 2nd. This just tells us that these 2 numbers are elements of their respective datasets, but unless we know how the datasets are ordered, this information alone isn't very useful.
When you sort the data in ascending order, the positions of the elements within the dataset start to have a meaning. For example, the 1st number would be the smallest, so you know that all other numbers must be equal or larger than it. The number positioned at the middle (the median) tells us that half of the other numbers in the dataset must have an equal or lower value, while the other half must be equal or greater. This is an effect from the sorting.
Let me give you a practical example: A gym teacher has a class of 21 students (the dataset). He wants to know their average height without doing any math. If he lines them up in a row by height, he can ask about, or measure, the height of the student in the middle (number 11, counting from left or right). Since they are ordered appropriately, this student's height would be the median, so half of the other students must be taller, while the other half must be shorter. The height of student 11 should be about average in this class.
Now, if the students gathered randomly in the row, this trick wouldn't work, since any one of them could have positioned themselves in the middle by chance. They wouldn't be sorted appropriately, so position 11 (middle) isn't guaranteed to be the actual median. It also wouldn't work if they sorted themselves by something other than height, like by their full names (alphabetically). I hope this makes sense.
Can you tell me in which situation Mean is preferred over Median?
when it comes to marks mean is better because the upper limit is set
I think median would be preferred to describe the price of a watch. As we know, there are some watch that are very expensive, far expensive from other watch. To describe the price, it would be preferred to use median
Median would be preferable in almost any case in which one wants to know the "average" price. For example, if I wanted to know how much a cup of coffee, in general, costs when I go abroad,, the median price will give me a better idea of how much I need. Reasoning,: there are crap cups of coffee (diners, inconvenience stores) and uber-high-end, specialty blends (such as those resulting from the beans that have traversed digestive tracts of small mammals, "harvested, and then finely ground into, what I can only presume, is one of those things one must acquire a taste for).
Nah, its a banging flavour without having to have tasted the medi-anus of different cups of coffee
who even drink coffe that traversed a digestive track 😵💫😵💫🤮🤮
matchmaking system in games: 2 teams have to fight but one team has (high low low low) players VS (medium medium medium medium) players
Are you talking about Dota?
@@anirudhranjan2934 haha, he forgot the 5th sample
probably the 5th sample went afk
Another similar case:
Followers of Instagram users.
We should choose the median as the most reflective measure of the central tendency since there are few proportions of celebrities with millions of followers while normal users might have hundreds.
I think when there is large variation in data median is preferable
In my understanding, per capita GDP is mean GDP. I think median GDP would be much more preferable as it would reflect the real life standard of living of the ordinary folks. [The mean incorporates the top 1% and hence pulls the per capita GDP upwards.]
Marks of students in difficult examination. In thos case md is prefered over mean
thats why college/uni should show median salary
Marks of students in a class. Most of the students get around avg. Marks while only a few manage to be exceptionally at the top by scoring high marks
Professional Salaries
Lotto dividends - a few people win the high divisions with most people winning the lower divisions.
Political parties tend to frame their electoral campaigns thinking on the median voter.
Income, wealth, living standard, poverty
College average salary package , Lottery ,
Lottery?
salary