Interpreting Box and Whisker Plots - Worksheet - BW2 - Free Printable

You've uploaded a completed worksheet titled “Interpreting Box-and-Whisker Plots”, and you’re asking me to solve the problem and explain the solution — even though the worksheet already has handwritten answers. I’ll walk through each part, validate the answers, and provide clear explanations so you understand *why* they’re correct.

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## 📊 Problem Overview

We are comparing snowboard prices at two stores:
- Middletown Snowboards: Prices = 345, 350, 356, 360, 375, 405
- Snowboard Central: Prices = 343, 370, 386, 392, 395, 402

We need to find the five-number summary, draw box plots, answer questions about medians, ranges, percentiles, and make a decision based on the data.

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## ✔ Part a) Identify the 5 main statistics of each set of data.

The five-number summary includes:
1. Minimum (Min)
2. First Quartile (Q1)
3. Median (Q2)
4. Third Quartile (Q3)
5. Maximum (Max)

🔹 Middletown Snowboards: [345, 350, 356, 360, 375, 405]

- Sorted? Yes.
- n = 6 → even number → median is average of 3rd and 4th values.

Step-by-step:

1. Min = 345 ✔️
2. Q1 = median of lower half → first 3 numbers: [345, 350, 356] → middle = 350 ✔️
3. Q2 (Median) = average of 3rd and 4th: (356 + 360)/2 = 358 ✔️
4. Q3 = median of upper half → last 3 numbers: [360, 375, 405] → middle = 375 ✔️
5. Max = 405 ✔️

✔ All answers correct.

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🔹 Snowboard Central: [343, 370, 386, 392, 395, 402]

Same process:

1. Min = 343 ✔️
2. Q1 = median of first 3: [343, 370, 386] → 370 ✔️
3. Q2 (Median) = (386 + 392)/2 = 389 ✔️
4. Q3 = median of last 3: [392, 395, 402] → 395 ✔️
5. Max = 402 ✔️

✔ All answers correct.

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## ✔ Part b) Draw a double box-and-whisker plot

You’ve drawn it correctly! Let’s verify the positions on the number line (scale: 340 to 410):

Middletown:

- Whisker from 345 to 405
- Box from Q1=350 to Q3=375
- Median line at 358 (inside box)

Central:

- Whisker from 343 to 402
- Box from Q1=370 to Q3=395
- Median line at 389

✔ Your sketch matches this. The box for Central is shifted right (higher prices), and Middletown’s box is wider and starts lower.

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## ✔ Part c) Answering specific questions

1. What is the median price for a snowboard at Middletown Snowboards?

> Q2 = $358

✔️ Correct. As calculated above.

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2. What is the lowest price you could pay for a snowboard at Snowboard Central?

> Min = $343

✔️ Correct.

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3. What is the most expensive board at Middletown Snowboards?

> Max = $405

✔️ Correct.

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4. What is the range of prices for snowboards at Snowboard Central?

> Range = Max - Min = 402 - 343 = $59

✔️ Correct.

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5. Which price represents the 75th percentile for Middletown Snowboards?

> Q3 = $375

✔️ Correct. The 75th percentile = third quartile (Q3).

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6. Which store would you rather buy a snowboard from? Why?

> Answer given: *Middletown Snowboards. Though the Max ($405) is very high, the majority of their snowboards are lower than Central’s. Notice the boxes.*

✔ This is a great, thoughtful answer!

#### 💡 Explanation:
- Median comparison: Middletown’s median is $358 vs Central’s $389 → Middletown’s *typical* price is cheaper.
- Box position: Middletown’s entire box (Q1 to Q3: $350–$375) lies *below* Central’s box ($370–$395).
- So even though Middletown has one outlier (the $405 board), most of its boards are cheaper than Central’s.
- Conclusion: If you want to save money, Middletown is better — unless you’re willing to pay more for higher-end boards (which Central seems to specialize in).

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## 🎯 Final Thoughts

This worksheet tests understanding of:
- Five-number summary
- Box plots as visual summaries
- Comparing distributions
- Making real-world decisions using statistics

All your answers are correct and well-reasoned. Great job!

If you’re reviewing this for a test or assignment, focus on:
- How to find quartiles with even/odd datasets
- What the box and whiskers represent
- How to compare two box plots visually and numerically

Let me know if you’d like to practice similar problems! 😊