Solved Interpreting a Box & Whisker Plot For questions - | Chegg.com - Free Printable

Let's solve each question step by step using the box-and-whisker plots provided in the worksheet.

---

First Box Plot: Test Scores (as %) for 9th Period

This box plot shows test scores as percentages. The key components of a box plot are:

- Minimum: Left end of the whisker
- Q1 (First Quartile): Left edge of the box
- Median (Q2): Line inside the box
- Q3 (Third Quartile): Right edge of the box
- Maximum: Right end of the whisker

From the graph:
- Minimum = 38
- Q1 = 72
- Median = 88
- Q3 = 96
- Maximum = 102

---

#### Question 1: What was the high score on the test?
The highest value is the maximum, which is at the right end of the whisker.

✔ Answer: 102

---

#### Question 2: What percent of the class scored above a 72?
72 is Q1 (first quartile). By definition, 25% of the data is below Q1, so 75% is above it.

✔ Answer: 75%

---

#### Question 3: What was the median score on the test?
The median is the line inside the box.

✔ Answer: 88

---

#### Question 4: What percent of the class scored between 88 & 96?
- 88 is the median (Q2).
- 96 is Q3.

So we're looking at the portion of the data between Q2 and Q3.

This is the top 25% of the data (since Q3 – Q2 covers the third quartile).

✔ Answer: 25%

---

#### Question 5: Do you think that this test was too hard for the students? Explain.

We can analyze based on the spread and central tendency.

- The median is 88, which is quite high — meaning half the class scored 88 or higher.
- The minimum is 38, which is low, but only one student (or a few) had that score.
- The interquartile range (IQR) is from 72 to 96 — most students scored in the 70s to 90s.
- The maximum is 102 (possibly extra credit), but the top 25% scored 96 or above.

Conclusion: Most students did well — median is high, and only a small portion scored very low. So the test likely wasn't too hard.

✔ Answer: No, the test was not too hard. The median score was 88%, indicating that half the class scored 88 or higher. Most students performed well, with only a few scoring below 72%.

---

Second Box Plot: Average Minutes Per Night Spent On Homework

This box plot shows time spent on homework per night.

From the graph:
- Minimum = 0
- Q1 = 20
- Median = 48
- Q3 = 60
- Maximum = 190

---

#### Question 7: What percent of the sophomores spend more than 60 minutes on homework per night?

60 is Q3. So 25% of students are above Q3.

✔ Answer: 25%

---

#### Question 8: What is the range of times that the middle 50% of the sophomores spend on homework per night?

The middle 50% is the interquartile range (IQR), from Q1 to Q3.

- Q1 = 20
- Q3 = 60

So the range is 20 to 60 minutes.

✔ Answer: 20 to 60 minutes

---

#### Question 9: How many sophomores do not do homework?

The minimum is 0, which means some students spent 0 minutes on homework.

But the box plot does not tell us how many students there are, nor how many exactly have 0 minutes. It only shows the distribution.

So we cannot determine the exact number from this graph.

✔ Answer: Cannot be determined from the graph.

---

#### Question 10: What percent of the sophomores spend less than 20 minutes per night on homework?

20 is Q1. So 25% of students are below Q1.

✔ Answer: 25%

---

✔ Final Answers Summary:

Test Scores (9th Period):
1. 102
2. 75%
3. 88
4. 25%
5. No, because the median is 88%, and most students scored above 72%. Only a few scored very low.

Homework Time (Sophomores):
7. 25%
8. 20 to 60 minutes
9. Cannot be determined
10. 25%

Let me know if you'd like a visual explanation or help interpreting box plots in general!