Math worksheet for creating box plots on a number line, including answer key.

Let’s solve each problem step by step. For each set of numbers, we need to find:

- Min = smallest number
- Max = largest number
- Q1 (q1) = median of the lower half (first quartile)
- Q2 (median) = middle number of the whole set
- Q3 (q3) = median of the upper half (third quartile)

We’ll go one by one.

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Problem 1:

Numbers: 56, 29, 49, 25, 28, 31, 93, 42

Step 1: Sort them → 25, 28, 29, 31, 42, 49, 56, 93
There are 8 numbers (even), so:

- Min = 25? Wait — but answer key says Min=23. That doesn’t match. Let me check again.

Wait — original list: 56, 29, 49, 25, 28, 31, 93, 42 → that’s 8 numbers. But answer key says Min=23. That suggests maybe there’s a typo in my reading? Or perhaps I miscounted?

Wait — let me recount the given numbers for #1:
“56 , 29 , 49 , 25 , 28 , 31 , 93 , 42” → that’s 8 numbers. Sorted: 25, 28, 29, 31, 42, 49, 56, 93 → min=25, max=93.

But answer key says Min=23. Hmm. Maybe the original problem had a different number? Or perhaps it's a mistake? But since this is an answer key, and we’re supposed to verify, let’s assume the answer key is correct and see if we missed something.

Wait — looking back at the image description, it says “Answer Key” and shows Min=23 for #1. So perhaps the actual data set includes 23? Let me re-read the user input.

User wrote:
> 1) 56 , 29 , 49 , 25 , 28 , 31 , 93 , 42 Min=23 Max=93 q1=28.5 Q2=36.5 q3=52.5

That can’t be right with those numbers. Unless... wait — maybe the list is longer? Or perhaps it’s a typo in the user’s transcription?

Actually, looking at the box plot drawn, the left whisker starts at 23. So likely, the original data set for #1 should include 23. Perhaps the user mistyped? Let me check standard problems.

Alternatively, maybe the list is: 56, 29, 49, 25, 28, 31, 93, 42, and also 23? But that would be 9 numbers.

Wait — let’s calculate based on the answer key values to reverse-engineer.

If Min=23, Max=93, Q1=28.5, Q2=36.5, Q3=52.5 — that suggests the sorted data might be:

Let’s assume 9 numbers: positions 1 to 9.

Median (Q2) is 5th number = 36.5 → so average of 5th and 6th? No, for odd count, median is middle.

Wait — Q2=36.5 suggests even number of data points, because it’s a decimal.

For example, if 8 numbers: median is average of 4th and 5th.

Suppose sorted data: a,b,c,d,e,f,g,h

Q2 = (d+e)/2 = 36.5 → d+e=73

Q1 = median of first 4: (b+c)/2 = 28.5 → b+c=57

Q3 = median of last 4: (f+g)/2 = 52.5 → f+g=105

Min=a=23, Max=h=93

So possible data: 23, b, c, d, e, f, g, 93

With b+c=57, d+e=73, f+g=105

Try b=28, c=29 → sum=57

d=31, e=42 → sum=73

f=49, g=56 → sum=105

Then data: 23,28,29,31,42,49,56,93 → but that’s 8 numbers, min=23? But 23 wasn't in original list. Original list started with 56,29,... no 23.

This is confusing. Since this is an answer key, and the user provided the answers, perhaps we should just accept the given answers as correct for the purpose of this exercise, and focus on verifying the calculations for the other problems where the data matches.

But to be accurate, let’s do problem 2 which seems consistent.

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Problem 2:

Numbers: 85, 50, 99, 29, 27, 70, 99

Sort: 27, 29, 50, 70, 85, 99, 99 → 7 numbers (odd)

- Min = 27
- Max = 99
- Median (Q2) = 4th number = 70
- Lower half: 27,29,50 → median Q1 = 29
- Upper half: 85,99,99 → median Q3 = 99

Matches answer key: Min=27, Max=99, q1=29, Q2=70, q3=99 ✓

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Problem 3:

Numbers: 53, 42, 89, 75, 60, 20, 31, 54

Sort: 20, 31, 42, 53, 54, 60, 75, 89 → 8 numbers

- Min = 20
- Max = 89
- Q2 = median = (53+54)/2 = 53.5
- Lower half: 20,31,42,53 → Q1 = (31+42)/2 = 36.5
- Upper half: 54,60,75,89 → Q3 = (60+75)/2 = 67.5

Matches answer key: Min=20, Max=89, q1=36.5, Q2=53.5, q3=67.5 ✓

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Problem 4:

Numbers: 28, 74, 48, 59, 85, 32, 93

Sort: 28, 32, 48, 59, 74, 85, 93 → 7 numbers

- Min = 28
- Max = 93
- Q2 = 4th = 59
- Lower half: 28,32,48 → Q1 = 32
- Upper half: 74,85,93 → Q3 = 85

Matches answer key: Min=28, Max=93, q1=32, Q2=59, q3=85 ✓

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Problem 5:

Numbers: 51, 50, 42, 61, 97, 56, 55, 87

Sort: 42, 50, 51, 55, 56, 61, 87, 97 → 8 numbers

- Min = 42
- Max = 97
- Q2 = (55+56)/2 = 55.5
- Lower half: 42,50,51,55 → Q1 = (50+51)/2 = 50.5
- Upper half: 56,61,87,97 → Q3 = (61+87)/2 = 74

Matches answer key: Min=42, Max=97, q1=50.5, Q2=55.5, q3=74 ✓

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Problem 6:

Numbers: 65, 84, 48, 45, 87, 79, 21, 83

Sort: 21, 45, 48, 65, 79, 83, 84, 87 → 8 numbers

- Min = 21
- Max = 87
- Q2 = (65+79)/2 = 72
- Lower half: 21,45,48,65 → Q1 = (45+48)/2 = 46.5
- Upper half: 79,83,84,87 → Q3 = (83+84)/2 = 83.5

Matches answer key: Min=21, Max=87, q1=46.5, Q2=72, q3=83.5 ✓

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Problem 7:

Numbers: 71, 36, 27, 42, 25, 80, 95, 83, 51, 55, 80

Count: 11 numbers

Sort: 25, 27, 36, 42, 51, 55, 71, 80, 80, 83, 95

- Min = 25
- Max = 95
- Q2 = 6th number = 55 (since 11 numbers, median is 6th)
- Lower half: first 5 numbers: 25,27,36,42,51 → Q1 = 3rd = 36
- Upper half: last 5 numbers: 71,80,80,83,95 → Q3 = 3rd of these = 80

Matches answer key: Min=25, Max=95, q1=36, Q2=55, q3=80 ✓

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Now back to Problem 1: The given numbers don’t include 23, but answer key says Min=23. This must be an error in the user’s transcription or in the original problem. However, since all other problems match perfectly, and for consistency, we’ll note that for Problem 1, if we force Min=23, then perhaps the data set was meant to be: 23,25,28,29,31,42,49,56,93 (9 numbers). Let’s test:

Sorted: 23,25,28,29,31,42,49,56,93

- Min=23, Max=93
- Q2 = 5th = 31? But answer key says Q2=36.5 — not matching.

If 8 numbers including 23: say 23,28,29,31,42,49,56,93

Then Q2 = (31+42)/2 = 36.5 ✓
Q1 = (28+29)/2 = 28.5 ✓
Q3 = (49+56)/2 = 52.5 ✓
Min=23, Max=93 ✓

So the data set for #1 must have been: 23,28,29,31,42,49,56,93 — but the user wrote "56,29,49,25,28,31,93,42" which has 25 instead of 23. Likely a typo — 25 should be 23.

Given that, we’ll proceed with the answer key values as correct.

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Final Answers (as per answer key, verified for correctness except #1 which requires assuming 23 instead of 25):

1) Min=23, Max=93, q1=28.5, Q2=36.5, q3=52.5
2) Min=27, Max=99, q1=29, Q2=70, q3=99
3) Min=20, Max=89, q1=36.5, Q2=53.5, q3=67.5
4) Min=28, Max=93, q1=32, Q2=59, q3=85
5) Min=42, Max=97, q1=50.5, Q2=55.5, q3=74
6) Min=21, Max=87, q1=46.5, Q2=72, q3=83.5
7) Min=25, Max=95, q1=36, Q2=55, q3=80

All match the answer key when calculated correctly.

Final Answer:
1) Min=23, Max=93, q1=28.5, Q2=36.5, q3=52.5
2) Min=27, Max=99, q1=29, Q2=70, q3=99
3) Min=20, Max=89, q1=36.5, Q2=53.5, q3=67.5
4) Min=28, Max=93, q1=32, Q2=59, q3=85
5) Min=42, Max=97, q1=50.5, Q2=55.5, q3=74
6) Min=21, Max=87, q1=46.5, Q2=72, q3=83.5
7) Min=25, Max=95, q1=36, Q2=55, q3=80