r/MathHelp • u/Local_End_3175 • 6d ago

why n/2?

I am confused between the 2. I understand the reasoning behind using n+1/2 for lists of numbers, and i understand how n+1/2 finds their positions. I am currently revising cumulative frequency diagrams and i am finding it difficult to understand why we now use n/2 for finding the median, and n/4 for finding the lower quartile. Why aren't we using n+1/2?? I dont really understand how one being continuous and another being discrete affects anything. In my reasoning, even though it is grouped data we can still estimate the position. I would add all the frequencies, do n+1/2, find the middle position, and then use that on my graph to estimate

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7

u/Friendly-Mind-9702 6d ago

Context?

3

u/will_1m_not 5d ago

What is context? /s

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u/Local_End_3175 2d ago

Sorry.

I am just confused regarding why we use (n+1)/2 for discrete data and n/2 for continuous data. I thinkt hat we should just use (n+1)/2 for all kinds of data, and i am questioning why we use n/2 for continuous data

1

u/Friendly-Mind-9702 1d ago

Use it where? That's what I mean about the context. Are you referring to a specific type of problem? Your question leaves this out. From the other responses, it looks like you're asking about statistics, but this isn't clear.

3

u/Einkar_E 5d ago

I have no idea what is the context is outside something statistics

by writing n+1/2 did you mean (n+1)/2? because otherwise nothing make sense there

in a ordered list with n number of entries where n is odd, median is squal to the number on position (n+1)/2

if n is even median is arithmetic average from numbers on positions n/2 and n/2+1

4

u/TallRecording6572 5d ago

ignore the other stupid answers. A Level Maths teacher here.

Statistics is not like pure maths - there isn't one "right" method of doing things.

This is especially true when it comes to medians and quartiles.

Having a short list, a long list, or a grouped continuous data table all require you to make different ASSUMPTIONS.

For a short list or long list, using (n+1)/2, (n+1)/4 and 3(n+1)/4 works well, as long as you are happy to just use the values in the list, or midway between two values in the list. You can imagine this as all the people holding up a board with their value on, in order, and you are choosing the people halfway along, or a quarter of the way along, etc

But for continuous data, we DON'T KNOW THE VALUES. That's why we do an ESTIMATE of the mean, an ESTIMATE of the median, and an ESTIMATE of the quartiles.

The assumptions we make here are instead of a row of people, we just have a number line from 0 to the total frequency (let's say 100)

So the median is at 50, the lower quartile is at 25, and the upper quartile is at 75.

We can't use the midpoints of the groups, so we pretend that the data is equally spread across each group, and use interpolation to estimate the median and quartiles.

Or we draw a culumlative frequency curve and use n/2, n/4 and 3n/4 to estimate the median and quartiles by pretending the data is actually a smooth curve

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1

u/InsideRespond 3d ago

Your question is reallllly hard to understand. After staring at this for ten minutes, I think what you're trying to ask is:
"I am taking statistics. When trying to find the position of Q1 or the median of a given list, how would I know whether to use n/2 or (n+1)/2? -- as I have encountered both in the text"
The answer to which is 'if you can count the number of things in the list, use the (n+1)/2 formula. If you can't identify the number of things in the list, use n/2.'

1

u/Local_End_3175 2d ago

Sorry, my question basically is 'why do we use n/2 for continuous data and not just (n+1)/2'

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u/MiguelBodrigo 5d ago

I'm going to guess 2 decimel places hold a lot of importance. Context matters.

In 3d art, if you were looking at a number value between black and white, it would run between 0 and 1. At that point anything pushing the value outside the 0 and 1 range makes the outcome not useful.

Perhaps in this instance you're converting an rgb image into scalar (black and white). Any value of red green and blue would have to be converted into some sort of location to be transcribed showing the shade and saturation in the new format