Dot Plots/Line Plots with Fractional Units Math Worksheets - Free Printable
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Step-by-step solution for: Dot Plots/Line Plots with Fractional Units Math Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Dot Plots/Line Plots with Fractional Units Math Worksheets
You've uploaded an answer key for “Interpreting Dot Plots Sheet 1,” which includes two dot plot problems with true/false/unknown evaluations. Since you asked to “solve the problem and explain the solution,” I’ll walk through each question in detail — not just state whether it’s true or false, but explain why, using the data from the dot plots.
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## 🔹 PROBLEM 1: Spelling Test Scores
Dot Plot Data (by score):
- Score 12 → 1 dot
- Score 14 → 2 dots
- Score 15 → 3 dots
- Score 16 → 5 dots
- Score 17 → 4 dots
- Score 18 → 3 dots
- Score 19 → 2 dots
- Score 20 → 1 dot
✔ Total number of students = 1 + 2 + 3 + 5 + 4 + 3 + 2 + 1 = 21 students
*(Note: The answer key says “UNKNOWN” for part b, but we can actually count the total dots — so this should be TRUE if it said 21, or FALSE if it said 20. Let’s analyze each part.)*
---
✔ TRUE
- The highest value on the x-axis with a dot is 20. So yes, 20 is the maximum score.
---
✘ FALSE (or UNKNOWN — depends on interpretation)
- The answer key says “UNKNOWN,” but that’s misleading. We can count the total number of dots = 21 students.
- If “marks” means “student scores recorded,” then there are 21 marks, not 20 → so it’s FALSE.
- If “marks” refers to possible points on the test (like a 20-point test), that’s not what the dot plot shows — it shows student scores, not test point total. So contextually, since it says “total of 20 marks in the test,” it likely means 20 student scores → which is wrong. So FALSE is more accurate.
> 📌 *Correction: Answer key should say FALSE here.*
---
✔ TRUE
- Mode = most frequent score.
- Score 16 has 5 dots — more than any other score → mode = 16.
---
✘ FALSE
- Range = Max – Min = 20 – 12 = 8.
- The answer key correctly says FALSE and explains: (20 – 12 = 8).
---
✔ TRUE
- Total students = 21 → half = 10.5 → so “half or more” would be 11+.
- Students scoring less than 17: scores 12, 14, 15, 16 → 1 + 2 + 3 + 5 = 11 students
- 11 out of 21 is more than half → so YES, more than half scored less than 17 → statement is TRUE.
> 💡 Note: The answer key says “8 out of 16 scored less” — that’s incorrect. It should be 11 out of 21. But the conclusion (TRUE) is correct.
---
✘ FALSE
- Median = middle value when ordered.
- With 21 students → median is the 11th score.
- Let’s list cumulative counts:
- 12 → 1st
- 14 → 2nd–3rd
- 15 → 4th–6th
- 16 → 7th–11th ← 11th score is 16
Wait! That suggests median is 16?
But the answer key says FALSE and claims median = (16 + 17)/2 = 16.5 — which would only be true if there were 22 students (even number).
Let’s recount total dots:
- 12: 1
- 14: 2 → total 3
- 15: 3 → total 6
- 16: 5 → total 11 ✔
- 17: 4 → total 15
- 18: 3 → total 18
- 19: 2 → total 20
- 20: 1 → total 21
So 21 students → 11th is the median → falls in score 16 → median = 16
> 🚨 The answer key is WRONG here. It incorrectly assumes 16 students (maybe miscounted). Actually, median is 16 → so statement is TRUE.
> 💡 Correction: This should be TRUE, not FALSE.
---
## 🔹 PROBLEM 2: Soccer Goals per Game
Dot Plot Data (by goals):
- 0 goals → 2 dots
- 1 goal → 2 dots
- 2 goals → 4 dots
- 3 goals → 3 dots
- 4 goals → 2 dots
- 5 goals → 2 dots
- 6 goals → 2 dots
✔ Total games = 2 + 2 + 4 + 3 + 2 + 2 + 2 = 17 games
*(Answer key says 15 — let’s check that later.)*
---
✘ FALSE
- There are 2 games with 0 goals → so they did NOT score in every match.
---
✔ TRUE
- Range = Max – Min = 6 – 0 = 6.
---
❓ UNKNOWN
- Dot plot shows goals scored, not wins/losses. You could score 6 goals and still lose if opponent scored 7. No info on wins → UNKNOWN.
---
✘ FALSE
- “Most” = more than half → half of 17 = 8.5 → need 9+ games.
- Games with < 3 goals: 0, 1, 2 → 2 + 2 + 4 = 8 games
- 8 < 9 → not most → FALSE.
> 💡 Answer key says “7 out of 15” — again, miscounting total games. Should be 8 out of 17 → still less than half → FALSE is correct.
---
✘ FALSE
- Total games = 17 → median is 9th score.
- Cumulative:
- 0 → 1st–2nd
- 1 → 3rd–4th
- 2 → 5th–8th
- 3 → 9th–11th ← 9th score is 3
→ Median = 3 → not 2 → FALSE.
> ✔ Answer key is correct here.
---
✔ TRUE
Let’s calculate mean:
Total goals =
- 0×2 = 0
- 1×2 = 2
- 2×4 = 8
- 3×3 = 9
- 4×2 = 8
- 5×2 = 10
- 6×2 = 12
Sum = 0 + 2 + 8 + 9 + 8 + 10 + 12 = 49
Mean = 49 ÷ 17 ≈ 2.88 → NOT 3
Wait — 49 ÷ 17 = 2.882… → not 3.
> 🚨 Answer key is WRONG here. Mean is approximately 2.88, not 3.
Unless… maybe they miscounted total games?
If total games = 15 (as answer key implies), then:
Let’s see: if we remove 2 games (say, both 0-goal games), total = 15, sum = 49 – 0 = 49 → 49/15 ≈ 3.27 → still not 3.
Alternatively, maybe they meant 3 as rounded? But 2.88 rounds to 3? Only if rounding to nearest whole number — but mean is usually reported with decimals unless specified.
> 💡 Conclusion: Statement is FALSE. Mean ≠ 3.
---
## ✔ FINAL CORRECTED ANSWER KEY:
a) TRUE
b) FALSE *(not UNKNOWN — total is 21, not 20)*
c) TRUE
d) FALSE
e) TRUE
f) TRUE *(median is 16, not 16.5 — answer key error)*
a) FALSE
b) TRUE
c) UNKNOWN
d) FALSE
e) FALSE
f) FALSE *(mean ≈ 2.88, not 3 — answer key error)*
---
## 🧠 Summary of Key Concepts:
- Mode: Most frequent value.
- Median: Middle value when ordered (for odd n, it’s the (n+1)/2 th value).
- Range: Max – Min.
- Mean: Sum of all values ÷ number of values.
- “Half” or “most”: Requires comparing to total count — must count accurately!
- Unknown: When data doesn’t support the claim (e.g., wins vs. goals).
---
## ⚠️ Important Note:
The original answer key contains several errors — especially in Problem 1 (f) and Problem 2 (f). Always double-check dot plot counts and calculations!
Let me know if you’d like me to create a corrected version of this worksheet or generate practice problems like this.
---
## 🔹 PROBLEM 1: Spelling Test Scores
Dot Plot Data (by score):
- Score 12 → 1 dot
- Score 14 → 2 dots
- Score 15 → 3 dots
- Score 16 → 5 dots
- Score 17 → 4 dots
- Score 18 → 3 dots
- Score 19 → 2 dots
- Score 20 → 1 dot
✔ Total number of students = 1 + 2 + 3 + 5 + 4 + 3 + 2 + 1 = 21 students
*(Note: The answer key says “UNKNOWN” for part b, but we can actually count the total dots — so this should be TRUE if it said 21, or FALSE if it said 20. Let’s analyze each part.)*
---
a) The maximum score on the test was 20.
✔ TRUE
- The highest value on the x-axis with a dot is 20. So yes, 20 is the maximum score.
---
b) There were a total of 20 marks in the test.
✘ FALSE (or UNKNOWN — depends on interpretation)
- The answer key says “UNKNOWN,” but that’s misleading. We can count the total number of dots = 21 students.
- If “marks” means “student scores recorded,” then there are 21 marks, not 20 → so it’s FALSE.
- If “marks” refers to possible points on the test (like a 20-point test), that’s not what the dot plot shows — it shows student scores, not test point total. So contextually, since it says “total of 20 marks in the test,” it likely means 20 student scores → which is wrong. So FALSE is more accurate.
> 📌 *Correction: Answer key should say FALSE here.*
---
c) The mode mark was 16.
✔ TRUE
- Mode = most frequent score.
- Score 16 has 5 dots — more than any other score → mode = 16.
---
d) The range of marks was 7.
✘ FALSE
- Range = Max – Min = 20 – 12 = 8.
- The answer key correctly says FALSE and explains: (20 – 12 = 8).
---
e) Half of the students scored less than 17 marks.
✔ TRUE
- Total students = 21 → half = 10.5 → so “half or more” would be 11+.
- Students scoring less than 17: scores 12, 14, 15, 16 → 1 + 2 + 3 + 5 = 11 students
- 11 out of 21 is more than half → so YES, more than half scored less than 17 → statement is TRUE.
> 💡 Note: The answer key says “8 out of 16 scored less” — that’s incorrect. It should be 11 out of 21. But the conclusion (TRUE) is correct.
---
f) The median mark was 16.
✘ FALSE
- Median = middle value when ordered.
- With 21 students → median is the 11th score.
- Let’s list cumulative counts:
- 12 → 1st
- 14 → 2nd–3rd
- 15 → 4th–6th
- 16 → 7th–11th ← 11th score is 16
Wait! That suggests median is 16?
But the answer key says FALSE and claims median = (16 + 17)/2 = 16.5 — which would only be true if there were 22 students (even number).
Let’s recount total dots:
- 12: 1
- 14: 2 → total 3
- 15: 3 → total 6
- 16: 5 → total 11 ✔
- 17: 4 → total 15
- 18: 3 → total 18
- 19: 2 → total 20
- 20: 1 → total 21
So 21 students → 11th is the median → falls in score 16 → median = 16
> 🚨 The answer key is WRONG here. It incorrectly assumes 16 students (maybe miscounted). Actually, median is 16 → so statement is TRUE.
> 💡 Correction: This should be TRUE, not FALSE.
---
## 🔹 PROBLEM 2: Soccer Goals per Game
Dot Plot Data (by goals):
- 0 goals → 2 dots
- 1 goal → 2 dots
- 2 goals → 4 dots
- 3 goals → 3 dots
- 4 goals → 2 dots
- 5 goals → 2 dots
- 6 goals → 2 dots
✔ Total games = 2 + 2 + 4 + 3 + 2 + 2 + 2 = 17 games
*(Answer key says 15 — let’s check that later.)*
---
a) The team scored at least one goal in every match.
✘ FALSE
- There are 2 games with 0 goals → so they did NOT score in every match.
---
b) The range of goals scored was 6.
✔ TRUE
- Range = Max – Min = 6 – 0 = 6.
---
c) The soccer team won most of their games.
❓ UNKNOWN
- Dot plot shows goals scored, not wins/losses. You could score 6 goals and still lose if opponent scored 7. No info on wins → UNKNOWN.
---
d) In most of their matches, the team scored less than 3 goals.
✘ FALSE
- “Most” = more than half → half of 17 = 8.5 → need 9+ games.
- Games with < 3 goals: 0, 1, 2 → 2 + 2 + 4 = 8 games
- 8 < 9 → not most → FALSE.
> 💡 Answer key says “7 out of 15” — again, miscounting total games. Should be 8 out of 17 → still less than half → FALSE is correct.
---
e) The median number of goals scored per game was 2.
✘ FALSE
- Total games = 17 → median is 9th score.
- Cumulative:
- 0 → 1st–2nd
- 1 → 3rd–4th
- 2 → 5th–8th
- 3 → 9th–11th ← 9th score is 3
→ Median = 3 → not 2 → FALSE.
> ✔ Answer key is correct here.
---
f) The mean score was 3 goals per match.
✔ TRUE
Let’s calculate mean:
Total goals =
- 0×2 = 0
- 1×2 = 2
- 2×4 = 8
- 3×3 = 9
- 4×2 = 8
- 5×2 = 10
- 6×2 = 12
Sum = 0 + 2 + 8 + 9 + 8 + 10 + 12 = 49
Mean = 49 ÷ 17 ≈ 2.88 → NOT 3
Wait — 49 ÷ 17 = 2.882… → not 3.
> 🚨 Answer key is WRONG here. Mean is approximately 2.88, not 3.
Unless… maybe they miscounted total games?
If total games = 15 (as answer key implies), then:
Let’s see: if we remove 2 games (say, both 0-goal games), total = 15, sum = 49 – 0 = 49 → 49/15 ≈ 3.27 → still not 3.
Alternatively, maybe they meant 3 as rounded? But 2.88 rounds to 3? Only if rounding to nearest whole number — but mean is usually reported with decimals unless specified.
> 💡 Conclusion: Statement is FALSE. Mean ≠ 3.
---
## ✔ FINAL CORRECTED ANSWER KEY:
Problem 1:
a) TRUE
b) FALSE *(not UNKNOWN — total is 21, not 20)*
c) TRUE
d) FALSE
e) TRUE
f) TRUE *(median is 16, not 16.5 — answer key error)*
Problem 2:
a) FALSE
b) TRUE
c) UNKNOWN
d) FALSE
e) FALSE
f) FALSE *(mean ≈ 2.88, not 3 — answer key error)*
---
## 🧠 Summary of Key Concepts:
- Mode: Most frequent value.
- Median: Middle value when ordered (for odd n, it’s the (n+1)/2 th value).
- Range: Max – Min.
- Mean: Sum of all values ÷ number of values.
- “Half” or “most”: Requires comparing to total count — must count accurately!
- Unknown: When data doesn’t support the claim (e.g., wins vs. goals).
---
## ⚠️ Important Note:
The original answer key contains several errors — especially in Problem 1 (f) and Problem 2 (f). Always double-check dot plot counts and calculations!
Let me know if you’d like me to create a corrected version of this worksheet or generate practice problems like this.
Parent Tip: Review the logic above to help your child master the concept of dot plots worksheets.
