Jayvion Caldwell

2022-07-16

Graph median, mode, range

The question is:
A scientist collects data. He determines both the mean of the data and the median of the data are equal to 7 and the data are symmetrical about this value. He starts to create a bar graph shown, but does not finish the graph.
If the range of the data is 8 and the maximum value of the data is 11, then how many data points fall above the value 7?
The answer is 14, but I don't know how this is the answer.

encoplemt5

Expert

Use the fact that the data are supposed to be symmetric about 7. So fill in stuff to make it symmetric, completing what the scientist did not get to finish. The symmetry automatically makes the mean and median equal to 7.
For symmetry, we need a black bar of height 7 at Value 8, to balance the black bar of height 7 at Value 6. We also need a black bar of height 4 at Value 9, to balance the black bar of height 4 at Value 5.
We also need a couple of short black bars on the left, to balance the short black bars at Values 10 and 11. These short black bars are at Values 4 and 3 respectively.
We already have range 8, So there is no more stuff to fill in. Now add up the heights of the black bars to the right of Value 7. We get 14.

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