Worksheet for interpreting box plots with statistical questions and data analysis.

It looks like you've uploaded a worksheet titled "Interpreting Box Plots Sheet 3", which contains two box plots and several questions related to interpreting them. Since I can't view images directly, I’ll help you solve the problems based on the description of what’s typically in such worksheets.

Let me walk through the likely content and solve it step by step.

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Box Plot 1: Time (in minutes) spent on homework by students

Assume the first box plot shows data about how long students spend on homework each night. Let's suppose the box plot has the following values (commonly found in such problems):

- Minimum: 20 minutes
- First Quartile (Q1): 30 minutes
- Median (Q2): 40 minutes
- Third Quartile (Q3): 50 minutes
- Maximum: 60 minutes

#### Questions and Answers:

1. The median time spent on homework is ______ minutes.
✔ Answer: 40 minutes
*(The median is the middle line in the box.)*

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2. The interquartile range (IQR) is ______ minutes.
✔ Answer: 20 minutes
*IQR = Q3 – Q1 = 50 – 30 = 20*

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3. The range of the data is ______ minutes.
✔ Answer: 40 minutes
*Range = Max – Min = 60 – 20 = 40*

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4. The longest time spent on homework was ______ minutes.
✔ Answer: 60 minutes
*(Maximum value)*

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5. The shortest time spent on homework was ______ minutes.
✔ Answer: 20 minutes
*(Minimum value)*

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6. What percent of students spent more than 50 minutes on homework?
✔ Answer: 25%
*Since Q3 = 50, only the top 25% are above that.*

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7. What percent of students spent less than 30 minutes on homework?
✔ Answer: 25%
*Below Q1 = 30 → bottom 25%*

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8. How many students spent between 30 and 50 minutes on homework?
This question requires knowing the total number of students. If not given, assume it's based on the box plot alone — but if we're told there are, say, 20 students:

→ Between Q1 and Q3 = 50% of the data
→ 50% of 20 = 10 students

✔ Answer: 10 students *(if total = 20)*
*(But if no total is given, answer may be “50%” or “half”)*

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Box Plot 2: Number of points scored by a basketball team in a game

Suppose this box plot shows points scored in games with these values:

- Min: 60
- Q1: 70
- Median: 80
- Q3: 90
- Max: 100

#### Questions and Answers:

9. The median number of points scored was ______.
✔ Answer: 80

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10. The interquartile range (IQR) is ______.
✔ Answer: 20
*IQR = 90 – 70 = 20*

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11. The range of the data is ______.
✔ Answer: 40
*100 – 60 = 40*

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12. How many games did the team score more than 90 points?
→ Above Q3 → top 25%
If total games = 20 → 25% of 20 = 5 games
✔ Answer: 5 games *(assuming 20 games)*

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13. What percent of games had fewer than 70 points?
→ Below Q1 → 25%
✔ Answer: 25%

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14. What percent of games had more than 80 points?
→ Above median → 50%
✔ Answer: 50%

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15. How many games had scores between 70 and 90?
→ Between Q1 and Q3 → 50%
If 20 games → 10 games
✔ Answer: 10 games *(if total = 20)*

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16. About how many games scored fewer than 60 points?
→ 60 is minimum → no games below → 0
✔ Answer: 0 games

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✔ Summary of Key Concepts:

- Median: Middle value
- Q1: 25th percentile
- Q3: 75th percentile
- IQR: Q3 – Q1 → spread of middle 50%
- Range: Max – Min
- Percentiles:
- < Q1 → 25%
- < Median → 50%
- > Q3 → 25%

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If your actual box plots have different numbers, please describe the values (min, Q1, median, Q3, max) for each, and I’ll adjust the answers accordingly.

Let me know!