Question

here is a data set:
68 75 64 72 73
65 72 78 69 55
73 56 60 57 63
60 60 66 64 64
you are examining the data with an expanded stem-and-leaf plot. here is the start of the plot:
5# | 567
6# | 0003444
6# | 5689
7# |
7# |
what should be entered in the second to last row of this table?
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Explanation:

Step1: Identify stem for 7# (first 7# row)

The stem - and - leaf plot has stems. For numbers in the 70s, the stem is 7. Let's list the data points in the 70s: 75, 72, 73, 72, 78, 73.

Step2: Sort the leaves (units digits)

First, we take the units digits of these numbers. For 75, the leaf is 5; for 72, the leaf is 2; for 73, the leaf is 3; for 72, the leaf is 2; for 78, the leaf is 8; for 73, the leaf is 3. Now we sort these leaves: 2, 2, 3, 3, 5, 8.

Step3: Determine the second - to - last row (first 7# row)

Looking at the stem - and - leaf plot structure, the rows are for different stems. The second - to - last row is the first row with stem 7 (since the last row is probably the second 7# row, but we need the second - to - last which is the first 7# row). The leaves for the first 7# row (stem 7, maybe for numbers from 70 - 74 or similar, but from the data, the numbers in the 70s are 72, 72, 73, 73, 75, 78. Wait, maybe the stem - and - leaf plot is using expanded stems where 7# is split into two rows: one for 70 - 74 and one for 75 - 79. Let's check:

Numbers in 70 - 74: 72, 73, 72, 73. Their leaves (units digits) are 2, 3, 2, 3. Sorting them: 2, 2, 3, 3.

Numbers in 75 - 79: 75, 78. Their leaves are 5, 8.

Looking at the given plot: 5# | 567 (numbers 55, 56, 57), 6# | 0003444 (numbers 60, 60, 60, 63, 64, 64, 64), 6# | 5689 (numbers 65, 66, 68, 69), 7# | (this is the second - to - last row, for 70 - 74), 7# | (last row, for 75 - 79).

So for the second - to - last row (stem 7, 70 - 74), the leaves are the units digits of 72, 72, 73, 73. Sorting them: 2, 2, 3, 3. So we need to enter the leaves as 2233 (or in order, sorted). Wait, the format of the previous rows: 5# | 567 (digits 5,6,7 for 55,56,57), 6# | 0003444 (digits 0,0,0,3,4,4,4 for 60,60,60,63,64,64,64), 6# | 5689 (digits 5,6,8,9 for 65,66,68,69). So for the 7# (second - to - last row, 70 - 74) numbers: 72,72,73,73. The units digits are 2,2,3,3. So we arrange them in ascending order: 2,2,3,3. So the entry should be 2233. Wait, let's check the data:

Data set: 68,75,64,72,73,65,72,78,69,55,73,56,60,57,63,60,60,66,64,64.

Wait, I missed some numbers. Let's list all numbers:

50s: 55,56,57 (so 5#, leaves 5,6,7)

60s: 60,60,60,63,64,64,64,65,66,68,69 (so 6# first row: 60,60,60,63,64,64,64 → leaves 0,0,0,3,4,4,4; 6# second row: 65,66,68,69 → leaves 5,6,8,9)

70s: 72,72,73,73,75,78 (so 7# first row: 72,72,73,73 → leaves 2,2,3,3; 7# second row: 75,78 → leaves 5,8)

So the second - to - last row is the first 7# row, which has leaves from 72,72,73,73. So the leaves are 2,2,3,3. So we enter them as 2233 (in the order of sorted leaves, as per the stem - and - leaf plot's previous rows which are sorted).

Answer:

2233