Question

1. (4 points) construct a stem-and-leaf display for the following data set, which presents amounts (in dollars) spent by 24 customers in a shop during a day. 57, 20, 27, 16, 11, 12, 29, 39, 45, 52, 58, 15, 46, 27, 22, 21, 15, 50, 16, 45, 20, 55, 12, 31

Explanation:

Step1: List all data points

First, we list out all the amounts spent: 57, 20, 27, 16, 11, 12, 29, 39, 45, 52, 58, 15, 46, 27, 22, 21, 15, 50, 16, 45, 20, 55, 12, 31. Wait, actually, the problem says 21 customers, let's count: first row (after 9) has 12 numbers: 57,20,27,16,11,12,29,39,45,52,58,15. Second row: 46,27,22,21,15,50,16,45,20,55,12,31. Wait, that's 12 + 12 = 24? Maybe a typo, but we'll proceed with the given numbers.

Step2: Determine stems (tens place)

The tens digits of the numbers: 1,2,3,4,5. So stems are 1,2,3,4,5.

Step3: List leaves (units place) for each stem

• Stem 1: Numbers with tens digit 1: 11,12,15,16,15,12,16. Wait, let's list all numbers with tens digit 1: 11,12,15,16,15,12,16? Wait, original data: 11,12,15,16,15,12,16? Wait, the numbers are: 11,12,15,16,12,15,16? Wait, let's go through each number:

Numbers: 57 (5), 20 (2), 27 (2), 16 (1), 11 (1), 12 (1), 29 (2), 39 (3), 45 (4), 52 (5), 58 (5), 15 (1), 46 (4), 27 (2), 22 (2), 21 (2), 15 (1), 50 (5), 16 (1), 45 (4), 20 (2), 55 (5), 12 (1), 31 (3). Now count: 24 numbers? Maybe the problem has a typo, but we'll proceed.

Now, group by stem (tens digit):

• Stem 1 (tens = 1): numbers are 11,12,16,15,12,15,16. Wait, 11,12,15,16,12,15,16? Wait, 11 (11), 12 (12), 16 (16), 15 (15), 12 (12), 15 (15), 16 (16). Wait, no, let's list each number's tens and units:

11: stem 1, leaf 1

12: stem 1, leaf 2

15: stem 1, leaf 5

16: stem 1, leaf 6

12: stem 1, leaf 2

15: stem 1, leaf 5

16: stem 1, leaf 6

Wait, but also 11,12,15,16,12,15,16? Wait, maybe I missed some. Wait the numbers with tens digit 1: 11,12,16,15,12,15,16? Wait, no, the original data (from the image): first row (after 9) has 12 numbers: 57,20,27,16,11,12,29,39,45,52,58,15. Second row: 46,27,22,21,15,50,16,45,20,55,12,31. So let's list all 24 numbers:

57,20,27,16,11,12,29,39,45,52,58,15,

46,27,22,21,15,50,16,45,20,55,12,31.

Now, separate by tens digit (stem) and units digit (leaf):

• Stem 1 (tens = 1):
• 11: leaf 1
• 12: leaf 2
• 16: leaf 6
• 15: leaf 5
• 12: leaf 2 (wait, second row has 12? Yes, second row: 12)
• 15: leaf 5 (second row: 15)
• 16: leaf 6 (second row: 16)

Wait, so numbers with stem 1: 11,12,16,15,12,15,16. Wait, that's 7 numbers? Wait 11,12,16,15,12,15,16: 7 numbers.

• Stem 2 (tens = 2):
• 20: leaf 0
• 27: leaf 7
• 29: leaf 9
• 27: leaf 7 (second row: 27)
• 22: leaf 2 (second row: 22)
• 21: leaf 1 (second row: 21)
• 20: leaf 0 (second row: 20)

So numbers: 20,27,29,27,22,21,20. Leaves: 0,7,9,7,2,1,0.

• Stem 3 (tens = 3):
• 39: leaf 9 (first row)
• 31: leaf 1 (second row)

So leaves: 9,1.

• Stem 4 (tens = 4):
• 45: leaf 5 (first row)
• 46: leaf 6 (second row)
• 45: leaf 5 (second row)

So leaves: 5,6,5.

• Stem 5 (tens = 5):
• 57: leaf 7 (first row)
• 52: leaf 2 (first row)
• 58: leaf 8 (first row)
• 50: leaf 0 (second row)
• 55: leaf 5 (second row)

So leaves: 7,2,8,0,5.

Step4: Organize stems and leaves (sort leaves for each stem)

• Stem 1:
• Leaves: 1,2,2,5,5,6,6 (sorted)
• So stem 1 | 1,2,2,5,5,6,6

• Stem 2:
• Leaves: 0,0,1,2,7,7,9 (sorted)
• Stem 2 | 0,0,1,2,7,7,9

• Stem 3:
• Leaves: 1,9 (sorted)
• Stem 3 | 1,9

• Stem 4:
• Leaves: 5,5,6 (sorted)
• Stem 4 | 5,5,6

• Stem 5:
• Leaves: 0,2,5,7,8 (sorted)
• Stem 5 | 0,2,5,7,8

Answer:

The stem - and - leaf display is as follows:

Stem	Leaf
2	0, 0, 1, 2, 7, 7, 9
3	1, 9
4	5, 5, 6
5	0, 2, 5, 7, 8