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Step-by-step solution for: Solved Interpreting a Box & Whisker Plot For questions - | Chegg.com
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Show Answer Key & Explanations
Step-by-step solution for: Solved Interpreting a Box & Whisker Plot For questions - | Chegg.com
Let’s solve each question step-by-step using the box-and-whisker plots provided.
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## 🔹 Part 1: Test Scores (as %) for 9th Period
The box plot shows:
- Minimum: 38
- Q1 (First Quartile): 72
- Median (Q2): 88
- Q3 (Third Quartile): 96
- Maximum: 102
*(Note: In a box plot, the left whisker is min, left edge of box is Q1, line inside box is median, right edge of box is Q3, and right whisker is max.)*
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✔ Answer: 102
> The highest value in the data set is shown at the end of the right whisker — that’s 102.
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✔ Answer: 75%
> 72 is Q1 (the first quartile). That means 25% of students scored *below* 72, so 75% scored above 72.
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✔ Answer: 88
> The median is the line inside the box — clearly labeled as 88.
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✔ Answer: 25%
> 88 is the median (Q2), and 96 is Q3. The box represents the middle 50% of the data (from Q1 to Q3). So from Q2 to Q3 is half of that 50%, which is 25%.
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✔ Answer: No, probably not.
> Explanation: The median score is 88%, which is a strong score (B+ or A- depending on grading scale). Also, 75% of students scored above 72%, which is typically a passing grade. Only 25% scored below 72, and the lowest score was 38 — which may be an outlier. Overall, most students performed well, suggesting the test was appropriately challenging, not “too hard.”
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## 🔹 Part 2: Average Minutes Per Night Spent On Homework (Sophomores)
Box plot shows:
- Minimum: 0
- Q1: 20
- Median: 48
- Q3: 60
- Maximum: 190
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✔ Answer: 25%
> 60 is Q3. That means 75% of students spend *less than or equal to* 60 minutes. So 25% spend more than 60 minutes.
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✔ Answer: 20 to 60 minutes
> The “middle 50%” is represented by the box — from Q1 to Q3. So that’s 20 to 60 minutes.
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✔ Answer: Cannot be determined from the box plot alone.
> Explanation: The minimum is 0, which means *at least one* student spends 0 minutes on homework. But we don’t know the total number of students or how many have a score of exactly 0. So unless told otherwise, we can’t say “how many” — only that some may not do homework.
> *However, if forced to give a numerical answer based on typical worksheet expectations, some teachers might accept “At least one” or “We cannot determine exact number.”*
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✔ Answer: 25%
> 20 is Q1 — meaning 25% of students spend *less than* 20 minutes on homework per night.
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## ✔ Final Answers Summary:
1. 102
2. 75%
3. 88
4. 25%
5. No, because the median is 88% and 75% scored above 72%, indicating most students did well.
7. 25%
8. 20 to 60 minutes
9. Cannot be determined exactly (or “At least one”)
10. 25%
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Let me know if you’d like a visual explanation or help drawing the box plots!
---
## 🔹 Part 1: Test Scores (as %) for 9th Period
The box plot shows:
- Minimum: 38
- Q1 (First Quartile): 72
- Median (Q2): 88
- Q3 (Third Quartile): 96
- Maximum: 102
*(Note: In a box plot, the left whisker is min, left edge of box is Q1, line inside box is median, right edge of box is Q3, and right whisker is max.)*
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1. What was the high score on the test?
✔ Answer: 102
> The highest value in the data set is shown at the end of the right whisker — that’s 102.
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2. What percent of the class scored above a 72?
✔ Answer: 75%
> 72 is Q1 (the first quartile). That means 25% of students scored *below* 72, so 75% scored above 72.
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3. What was the median score on the test?
✔ Answer: 88
> The median is the line inside the box — clearly labeled as 88.
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4. What percent of the class scored between 88 & 96?
✔ Answer: 25%
> 88 is the median (Q2), and 96 is Q3. The box represents the middle 50% of the data (from Q1 to Q3). So from Q2 to Q3 is half of that 50%, which is 25%.
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5. Do you think that this test was too hard for the students? Explain.
✔ Answer: No, probably not.
> Explanation: The median score is 88%, which is a strong score (B+ or A- depending on grading scale). Also, 75% of students scored above 72%, which is typically a passing grade. Only 25% scored below 72, and the lowest score was 38 — which may be an outlier. Overall, most students performed well, suggesting the test was appropriately challenging, not “too hard.”
---
## 🔹 Part 2: Average Minutes Per Night Spent On Homework (Sophomores)
Box plot shows:
- Minimum: 0
- Q1: 20
- Median: 48
- Q3: 60
- Maximum: 190
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7. What percent of the sophomores spend more than 60 minutes on homework per night?
✔ Answer: 25%
> 60 is Q3. That means 75% of students spend *less than or equal to* 60 minutes. So 25% spend more than 60 minutes.
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8. What is the range of times that the middle 50% of the sophomores spend on homework per night?
✔ Answer: 20 to 60 minutes
> The “middle 50%” is represented by the box — from Q1 to Q3. So that’s 20 to 60 minutes.
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9. How many sophomores do not do homework?
✔ Answer: Cannot be determined from the box plot alone.
> Explanation: The minimum is 0, which means *at least one* student spends 0 minutes on homework. But we don’t know the total number of students or how many have a score of exactly 0. So unless told otherwise, we can’t say “how many” — only that some may not do homework.
> *However, if forced to give a numerical answer based on typical worksheet expectations, some teachers might accept “At least one” or “We cannot determine exact number.”*
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10. What percent of the sophomores spend less than 20 minutes per night on homework?
✔ Answer: 25%
> 20 is Q1 — meaning 25% of students spend *less than* 20 minutes on homework per night.
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## ✔ Final Answers Summary:
Part 1: Test Scores
1. 102
2. 75%
3. 88
4. 25%
5. No, because the median is 88% and 75% scored above 72%, indicating most students did well.
Part 2: Homework Time
7. 25%
8. 20 to 60 minutes
9. Cannot be determined exactly (or “At least one”)
10. 25%
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Let me know if you’d like a visual explanation or help drawing the box plots!
Parent Tip: Review the logic above to help your child master the concept of box and whisker plot worksheet 1.
