Interpreting Box-and-Whisker Plots Worksheet featuring two graphs: average monthly high temperatures in Milwaukee and test scores for 9th period math, with questions to analyze the data.

Let's solve each part of this Interpreting Box-and-Whisker Plots Worksheet step by step.

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Question 1: Complete the table using the box-and-whisker plot for Milwaukee.

We are given a box-and-whisker plot for Average Monthly High Temperatures in Milwaukee.

The plot shows:

- Left whisker ends at 26
- Box starts at 35
- Median line is at 57
- Box ends at 73
- Right whisker ends at 80

#### Definitions:
- Minimum: The smallest value (left end of the left whisker)
- Maximum: The largest value (right end of the right whisker)
- Median: The middle value (line inside the box)
- Lower Quartile (Q1): The left edge of the box
- Upper Quartile (Q3): The right edge of the box
- Interquartile Range (IQR): Q3 - Q1

Now fill in the table:

| | Milwaukee |
|-------------------|-----------|
| Minimum | 26 |
| Maximum | 80 |
| Median | 57 |
| Lower Quartile| 35 |
| Upper Quartile| 73 |
| Interquartile Range | 73 - 35 = 38 |

✔ So, the completed table is:

| | Milwaukee |
|-------------------|-----------|
| Minimum | 26 |
| Maximum | 80 |
| Median | 57 |
| Lower Quartile | 35 |
| Upper Quartile | 73 |
| Interquartile Range | 38 |

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Questions 2–6: Test Scores (as %) for 9th Period

We have a second box-and-whisker plot with the following values:

- Left whisker: 38
- Box starts at: 72
- Median line: 88
- Box ends at: 96
- Right whisker: 102

So:
- Min = 38
- Q1 = 72
- Median = 88
- Q3 = 96
- Max = 102

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#### Question 2: What was the high score on the test?

The highest score is the maximum, which is at the end of the right whisker.

> ✔ Answer: 102

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#### Question 3: What percent of the class scored above a 72?

- 72 is the lower quartile (Q1).
- By definition, 25% of the data lies below Q1.
- So, 75% of the data lies above Q1.

> ✔ Answer: 75%

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#### Question 4: What was the median score on the test?

The median is the line inside the box.

> ✔ Answer: 88

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#### Question 5: What percent of the class scored between 88 and 96?

- 88 is the median (Q2)
- 96 is the upper quartile (Q3)

The range from median to Q3 represents the top 25% of the data.

> ✔ Answer: 25%

(Explanation: From Q2 to Q3 is the third quartile — 25% of the data.)

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#### Question 6: Do you think that this test was too hard for the students? Explain.

Let’s analyze the data:

- Minimum: 38 → some students did very poorly
- Q1 (25th percentile): 72 → 25% scored 72 or below
- Median (50th percentile): 88 → half the class scored 88 or below
- Q3 (75th percentile): 96 → 75% scored 96 or below
- Maximum: 102

This means:
- Only 25% of students scored below 72
- Half the class scored at or above 88
- Most students scored highly, especially since 75% scored 96 or lower, but note: 96 is still high

But wait — the lowest score was 38, which is low, but only one student likely had that.

However, the median is 88, which is a strong grade, suggesting most students performed well.

➡️ Interpretation: While there was one very low score, the majority of students did well. The median is high (88), and the upper half of the class scored between 88 and 102.

> ✔ Answer: No, the test was not too hard.
> The median score was 88%, and 75% of students scored 72 or higher. Most students performed well, indicating the test was fair or even easy for many. The low score of 38 may be an outlier, but it doesn't reflect the overall performance.

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✔ Final Answers Summary:

#### Question 1: Milwaukee Table
| | Milwaukee |
|-------------------|-----------|
| Minimum | 26 |
| Maximum | 80 |
| Median | 57 |
| Lower Quartile | 35 |
| Upper Quartile | 73 |
| Interquartile Range | 38 |

#### Question 2: High score = 102

#### Question 3: Percent above 72 = 75%

#### Question 4: Median score = 88

#### Question 5: Percent between 88 and 96 = 25%

#### Question 6:
No, the test was not too hard. The median score was 88%, meaning half the class scored 88 or higher. Additionally, 75% of students scored 72 or above, and the top 25% scored between 88 and 102. Although one student scored very low (38), the majority performed well, indicating the test was manageable for most students.

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