Kenneth S. answered • 02/26/16
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If only one DIGIT changes, accounting for reduction of 30 hairs, then it has to be that 75 was wrong & should have been 45. This gives the correct average (mean).
You are to be commended for a very good job of analysis, and good typing and presentation of this problem.
Kenneth S.
I liked 74 (changing to 45) because there already was a 45 in the table.
But 40 changed to 10 also works (& there's already a 10 in the table).
Either of these would effect the minimum change in the table's LEAF part, by not introducing a leaf number that was not already there. (This is my interpretation of the "one digit in the stem-and-leaf table is incorrect.)
For any others that COULD be reduced by 30, the reduced result would not duplicate a number already in the table.
Quite an interesting problem; as so often is the case, it comes down to a question of semantics.
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02/26/16
Ravi B.
Sorry for the late response; I just saw the question. First, let's recall what the stem-and-leaf plot originally looked like:
0 | 1 1 3 5 6 8
1 | 0 2 2 2 4
2 | 3 9
4 | 0 5
5 | 6 8
7 | 5 6 9
Elena, as you pointed out, we need a reduction of 30. We can change only one digit in the table. We can change the tens digit 7 to a 6 (not 4), which reduces the three entries on 7's row by 10 each, for a total reduction of 30. The 7's row is the only row with either 1 or 3 entries, so that's the only change that works.
P.S. I'm a co-author of the book. Elena, do you have our solutions manual?
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05/15/16
Elena K.
02/26/16