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# Mean and Median watch

1. Hello

This looks a really easy question but i dont actually know the answer. Could someone please tell me how i work it out...
Do i just add them all up and divide by 5? So the answer is 3.18?

The five number summary for the weights (in pounds) of fish caught in a bass tournament is:

Min: 2.3
Q1: 2.8
Medium: 3.0
Q3: 3.3
Max: 4.5

Would you expect the mean weight of all the fish caught to be higher or lower than the median? Explain

Thanks
2. the mean is the sum of all the pieces of data divided by the amount of data there is.

the median is just the middle piece of data, so it could either higher, lower or equal to the mean; it all depends on the value of the data

so in this case yes, the mean is 3.18 which would make it higher than the median
3. (Original post by Rooster523)
the mean is 3.18
You can't possibly know that, you haven't been given the data.

You're expected to look for signs of skew. Is the data more concentrated towards the lower end or the higher end? What would this do to the mean?
4. (Original post by generalebriety)
You can't possibly know that, you haven't been given the data.
i knew there was a reason i didn't take stats at AS
5. oh so because the distance from the minimum weight to the middle weight is 3.0-2.3= 0.7 pounds while the distance from the middle weight to the maximum weight is 4.5-3.0= 1.5 pounds.

So it is higher than the median?
6. I would have thought it would be slightly higher than the median.

But obviously thats a guess because we don't know the data.

I base this because the mid point of the inter quartile ranges is 3.05 and the midpoint of the highest and lowest is 3.4.
7. (Original post by anon2332)
oh so because the distance from the minimum weight to the middle weight is 3.0-2.3= 0.7 pounds while the distance from the middle weight to the maximum weight is 4.5-3.0= 1.5 pounds.

So it is higher than the median?
Yep, that'd be my guess. Of course, it is only a guess, because we don't know the data, but it's a sensible one.
8. In your answer I'd draw a box plot to illustrate the data.

At S1 level a you can use the quartiles for a simple acceptable way to describe the shape of the data(skewness) by comparing the value of Q2-Q1 with Q3-Q2 (where Q2 is the median).
If Q2-Q1 = Q3-Q2 then it's a symmetrical distribution and the mean = median.
If Q2-Q1 < Q3-Q2 this indicates positive skew and a median < mean.
If Q2-Q1 > Q3-Q2 this indicates negative skew and a median > mean.

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