Question

tennis and golf: following are the ages of the winners of the mens wimbledon tennis championship and the masters golf championship for the years 1970 through 2023. (there was no wimbledon tournament in 2020.)
ages of wimbledon winners
20 21 22 23 24 22 29 24 25 17
18 22 22 21 24 22 21 21 22 23
26 25 26 27 28 31 21 21 22 23
24 25 22 27 24 24 30 26 27 28
29 35 31 32 34 35 20
ages of masters winners
33 27 42 27 23 31 28 26 32 27
46 28 30 31 32 33 35 28 43 29
38 23 41 33 37 25 26 33 32 21
33 31 28 39 39 26 33 35 21 29
28 37 27 43 35 29 25 28
(a) construct back - to - back split stem - and - leaf plots for these data sets, in which each stem appears twice, once for leaves 0 - 4 and again for leaves 5 - 9. do not separate the answers with commas. if there are no leaves on a particular stem, select the
one\ button.
wimbledon
masters
none
part: 0 / 2
part 1 of 2
send data to excel

Answer:

Ages of Wimbledon Winners Stem - and - Leaf Plot (Back - to - Back, Split Stem)

Step 1: Identify the stems

The ages range from 17 to 35. So the stems will be 1, 2, 3. But we use split stems, so we will have stems 1, 2 (for leaves 0 - 4), 2 (for leaves 5 - 9), 3 (for leaves 0 - 4), 3 (for leaves 5 - 9)

Step 2: Organize the data for Wimbledon Winners

First, list all the ages of Wimbledon Winners: 20, 21, 22, 23, 24, 22, 29, 24, 25, 18, 22, 22, 21, 24, 22, 22, 21, 22, 23, 20, 21, 22, 22, 23, 24, 25, 26, 25, 26, 27, 28, 24, 24, 27, 28, 26, 27, 28, 29, 35, 31, 32, 34, 35, 20

Now, split the data by stems and leaves (0 - 4 and 5 - 9):

• Stem 1:
• Leaves (0 - 4): None (since the only age with stem 1 is 18, leaf = 8 which is in 5 - 9)
• Leaves (5 - 9): 8 (from 18)
• Stem 2 (leaves 0 - 4):
• Ages with stem 2 and leaf 0 - 4: 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24
• Sort the leaves: 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4
• Stem 2 (leaves 5 - 9):
• Ages with stem 2 and leaf 5 - 9: 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28, 28, 29, 29
• Sort the leaves: 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9
• Stem 3 (leaves 0 - 4):
• Ages with stem 3 and leaf 0 - 4: 31, 32, 34
• Sort the leaves: 1, 2, 4
• Stem 3 (leaves 5 - 9):
• Ages with stem 3 and leaf 5 - 9: 35, 35
• Sort the leaves: 5, 5

Now, construct the back - to - back stem - and - leaf plot (we will assume the Masters data will be done similarly, but for part (a) we focus on Wimbledon first). The stem - and - leaf plot for Wimbledon (back - to - back will be completed when we do Masters, but for the first part, the Wimbledon stem - and - leaf with split stems is:

Stem	Leaves (0 - 4)	Leaves (5 - 9)
2	0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4	5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9
3	1, 2, 4	5, 5

Ages of Masters Winners Stem - and - Leaf Plot (Back - to - Back, Split Stem)

The ages of Masters Winners: 33, 27, 42, 27, 23, 31, 28, 26, 32, 33, 35, 28, 43, 37, 27, 43, 35, 29, 25, 28, 33, 27, 28, 30, 31, 32, 33, 37, 25, 26, 32, 31, 29, 38, 23, 41, 33, 37, 25, 26, 32, 31, 29, 33, 31, 28, 39, 39, 26, 33, 32, 35, 21, 37, 27, 43, 35, 29, 25, 28, 46, 28, 30, 31, 32, 35, 28, 43

Now, split the data by stems and leaves (0 - 4 and 5 - 9):

• Stem 2:
• Leaves (0 - 4): 21, 23, 23, 25, 25, 25, 26, 26, 26
• Sort the leaves: 1, 3, 3, 5, 5, 5, 6, 6, 6
• Leaves (5 - 9): 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 29, 29, 29
• Sort the leaves: 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9
• Stem 3:
• Leaves (0 - 4): 30, 30, 31, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33, 33, 33
• Sort the leaves: 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3
• Leaves (5 - 9): 35, 35, 35, 35, 37, 37, 37, 38, 39, 39
• Sort the leaves: 5, 5, 5, 5, 7, 7, 7, 8, 9, 9
• Stem 4:
• Leaves (0 - 4): 41, 43, 43, 43, 43
• Sort the leaves: 1, 3, 3, 3, 3
• Leaves (5 - 9): 46
• Sort the leaves: 6

Now, the stem - and - leaf plot for Masters (split stem) is:

Stem	Leaves (0 - 4)	Leaves (5 - 9)
3	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3	5, 5, 5, 5, 7, 7, 7, 8, 9, 9
4	1, 3, 3, 3, 3	6

Back - to - Back Stem - and - Leaf Plot

Now, construct the back - to - back plot with Wimbledon on the left and Masters on the right, split stems:

Wimbledon (leaves 0 - 4)	Stem	Masters (leaves 0 - 4)	Wimbledon (leaves 5 - 9)	Stem	Masters (leaves 5 - 9)
0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4	2	1, 3, 3, 5, 5, 5, 6, 6, 6	5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9	2	7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9
1, 2, 4	3	0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3		3	5, 5, 5, 5, 7, 7, 7, 8, 9, 9
	4	1, 3, 3, 3, 3		4	6

(Note: This is a detailed construction. If we were to present the back - to - back plot in a more standard format, we would have the stem in the middle, Wimbledon leaves on the left (sorted) and Masters leaves on the right (sorted) for each split stem (0 - 4 and 5 - 9))

For example, the back - to - back split stem - and - leaf plot (abbreviated) would look like:

Wimbledon (0 - 4)	Stem	Masters (0 - 4)	Wimbledon (5 - 9)	Stem	Masters (5 - 9)
0,0,0,1,1,1,1,2,...	2	1,3,3,5,5,5,6...	5,5,5,6,6,6,7,...	2	7,7,7,7,8,8,...
1,2,4	3	0,0,1,1,1,1,2...		3	5,5,5,5,7,7,...
	4	1,3,3,3,3		4	6

Since the question asks to construct the back - to - back split stem - and - leaf plots, the above is the step - by - step construction.

(If we were to present the final plot in a boxed format, but since it's a plot, we can summarize the key stems and leaves. However, following the step - by - step, we have constructed the plot as above)

Final Answer (for the construction of back - to - back split stem - and - leaf plots)

The back - to - back split stem - and - leaf plots are constructed as shown above, with stems 1, 2 (split into 0 - 4 and 5 - 9), 3, 4, Wimbledon leaves on the left, and Masters leaves on the right, sorted for each stem - leaf group.