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Question: Write a few sentences comparing the distributions of P-T ratios for states in the two groups (west and east) during the 2001–2002 school year.

Sample solution:

The shapes of the two histograms are different. The histogram for states that are west of the Mississippi River is unimodal and skewed to the right, whereas the histogram for states that are east of the Mississippi River is unimodal and nearly symmetric.

As noted in part (a), the medians of the two distributions are about the same, between 15 and 16 for both distributions.

The histograms also show that there is more variability in the P-T ratios for states that are west of the Mississippi River. Although the greatest and least values for each group are not known, the range can be approximated. The range for the west is at most 22 - 12 = 10, and the range for the east is at most 19 -12 = 7.

Why are they unknown? for West I think the greatest P-T ratio is 22 and least is 12. Whereas for East, the greatest P-T ratio is 19 and least is 12.

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up vote 0 down vote accepted

As the data has been binned into whole number bins, then we have no information as to where the particular ratios lie within those intervals.

The most we can say is that for the West group, the lowest P/T ratio lies between 12 and 13 and the highest ratio between 21 and 22; and for the East group, the lowest ratio is between 12 and 13, and the highest between 18 and 19.

So to calculate the approximate ranges, we take the extreme values in these intervals - the highest the highest ratio could possibly be (e.g. for the West, this is 22) and the lowest the lowest P/T ratio could be (again for the West, this is 12), giving the maximum range for the West of 22-12=10. Similarly for the East group (19-12=7)

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