Could you explain what a quartile and median are?

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other_letter2017-07-11 17:58:43

Mathematics

other_letter, 2017-07-11 17:58:43

Such are the things.
I collected a lot of data on processing a bunch of similar operations.
There is a cost, a deadline, a performer... a lot of things.
But I can’t get enough of the usefulness of the quartile (top / bottom) and median indicators.
Let's say I represent a set of records in the context of time (how long the work was done).
1. Minimum and maximum - simple: 50 and 500 hours.
2. The arithmetic mean is also understandable: 160 hours.
3. Top. quartile - 170 hours.
4. Lower - 130 hours.
5. Median - 150 hours
Do you mind explaining what that means?
Clause 1 is clear to everyone.
p.2 how much on average, taking into account the entire shaft. Let's say the most likely value if nothing is done.
What are the quartiles talking about?
Is the probability of hitting over/under less than 20%? (this is a gag)
And the median?
Clarify please. Google works, I even remember how to calculate it. But what it means and how to apply it in life - I do not understand.

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3 answer(s)

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Mercury13, 2017-07-11
@Mercury13

This means:
The bottom 25% of jobs are in the 50…130 range.
The next 25% are in the range of 130…150
Another 25% are in the range of 150…170
AND the top 25% of works are in the range of 170…500
The fact that the mean is above the median usually indicates that the distribution has a “long tail” on top. As you can see, as many as 25% of the works fall into the range of 170…500.

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Dimonchik, 2017-07-11
@dimonchik2013

well, the median is also a quartile
and it says everything about the fact that if not you, but employees work for 150 hours, closer to 170

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dmshar, 2017-07-11
@dmshar

If the data is not distributed according to the normal distribution law (and they are almost always so distributed, just in some cases it is close to normal, and in others it is not), then just the arithmetic mean is an uninformative value, unlike the median.
Illustrative example:
Salary by enterprise
- $100, $110, $120, $130, $140, $150, $160, $170, $200, $250, $900
Average - 220.9. What is she talking about? Yeah, the average salary is quite decent :-)
Medina - 150. Quite understandable - half of the people get less, the other half more.
Quartiles are a division of the sample into four parts equal in the number of elements in them.
From your data, by the way, it is clear that they are not very normal.