Please help me fast: mean, median, and mode
- Thread starter Scarpetta
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- Feb 4, 2004
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There are infinitely-many "right" answers to this question. Just pick some numbers clustered around the given median value, make sure you have more of the mode value than any other value, and then tweak the values to make sure the mean comes out right.
There is no formula. You just have to take some time and fiddle with the numbers.
Eliz.
__________
Edit: Ne'mind. Answer posted below.
There is no formula. You just have to take some time and fiddle with the numbers.
Eliz.
__________
Edit: Ne'mind. Answer posted below.
Hello, Scarpetta!
Since the mean is 85, it is as if all five numbers are 85.
\(\displaystyle \;\;\)Note that their sum is: \(\displaystyle \,5\,\times\,85\:=\:425\).
We'll start with that set of numbers: \(\displaystyle \,\begin{pmatrix}85 \\ 85 \\ 85 \\ 85 \\ 85\end{pmatrix}{\)
Since the median will be 84, we'll make 84 the middle number: \(\displaystyle \;\begin{pmatrix}85 \\ 85 \\ 84 \\ 85 \\ 85\end{pmatrix}\)
But we just lost 1 from our total (425), so we must add 1 to another number, say, the top one.
\(\displaystyle \;\;\)Then we have: \(\displaystyle \,\begin{pmatrix}86 \\ 85 \\ 84 \\ 85 \\ 85 \\ 85\end{pmatrix}\)
Since the mode will be 82, make the bottom two numbers 82: \(\displaystyle \;\;\begin{pmatrix}86\\ 85 \\ 84 \\ 82 \\ 82 \end{pmatrix}\)
But we lost 6 from our total. so we must add 6 to the upper numbers.
Let's say, add 3 to the top number and 3 to the next number.
Therefore. we have: \(\displaystyle \;\begin{pmatrix}89 \\ 88 \\ 84 \\ 82 \\ 82\end{pmatrix}\;\;\) . . . ta-DAA!
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Check
Mean: \(\displaystyle \,\frac{89\,+\,88\,+\,84\,+\,82\,+\,82}{5}\:=\:\frac{425}{5}\;=\;85\)
Median: \(\displaystyle \;\)The "middle" score is 84.
Mode: \(\displaystyle \;\)The most frequent score is 82.
\(\displaystyle \;\;\) . . . We're golden!
Here's a method that requires no guessing . . .
Since the mean is 85, it is as if all five numbers are 85.
\(\displaystyle \;\;\)Note that their sum is: \(\displaystyle \,5\,\times\,85\:=\:425\).
We'll start with that set of numbers: \(\displaystyle \,\begin{pmatrix}85 \\ 85 \\ 85 \\ 85 \\ 85\end{pmatrix}{\)
Since the median will be 84, we'll make 84 the middle number: \(\displaystyle \;\begin{pmatrix}85 \\ 85 \\ 84 \\ 85 \\ 85\end{pmatrix}\)
But we just lost 1 from our total (425), so we must add 1 to another number, say, the top one.
\(\displaystyle \;\;\)Then we have: \(\displaystyle \,\begin{pmatrix}86 \\ 85 \\ 84 \\ 85 \\ 85 \\ 85\end{pmatrix}\)
Since the mode will be 82, make the bottom two numbers 82: \(\displaystyle \;\;\begin{pmatrix}86\\ 85 \\ 84 \\ 82 \\ 82 \end{pmatrix}\)
But we lost 6 from our total. so we must add 6 to the upper numbers.
Let's say, add 3 to the top number and 3 to the next number.
Therefore. we have: \(\displaystyle \;\begin{pmatrix}89 \\ 88 \\ 84 \\ 82 \\ 82\end{pmatrix}\;\;\) . . . ta-DAA!
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Check
Mean: \(\displaystyle \,\frac{89\,+\,88\,+\,84\,+\,82\,+\,82}{5}\:=\:\frac{425}{5}\;=\;85\)
Median: \(\displaystyle \;\)The "middle" score is 84.
Mode: \(\displaystyle \;\)The most frequent score is 82.
\(\displaystyle \;\;\) . . . We're golden!