Math homework worksheet featuring a box and whisker plot of test scores for 6th period, with questions on statistical analysis.

Let’s solve each question step by step, using the box-and-whisker plots provided.

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First Plot: Test Scores (as %) for 6th Period

The plot shows:
- Minimum = 38
- Q1 (first quartile) = 72
- Median (Q2) = 88
- Q3 (third quartile) = 96
- Maximum = 102

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Question 1: What was the high score on the test?

→ The highest value in a box-and-whisker plot is the end of the right whisker.
→ That’s 102.

✔ Answer: 102

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Question 2: What percent of the class scored above a 72?

→ 72 is Q1 (first quartile).
→ By definition, 25% of data is below Q1, so 75% is above Q1.

✔ Answer: 75%

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Question 3: What was the median score on the test?

→ The median is the middle line inside the box.
→ It’s labeled as 88.

✔ Answer: 88

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Question 4: What percent of the class scored between 88 & 96?

→ 88 is the median (Q2), and 96 is Q3.
→ Between Q2 and Q3 is exactly 25% of the data.

✔ Answer: 25%

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

→ Let’s look at the scores:
- Lowest score: 38 → pretty low
- But median is 88 → half the class did very well
- Q1 is 72 → even the lower quarter did okay
- Only one student got below 72? Not necessarily — but 25% scored below 72.
- However, 75% scored 72 or higher, and 50% scored 88 or higher.

→ So most students did well. A few struggled (like the 38), but overall, it doesn’t seem “too hard” — maybe just challenging for some.

✔ Answer: No, because the median score was 88, which means half the class scored 88 or higher. Most students did well, though a few had lower scores.

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Question 6: Would you expect the mean to be above or below the median? Explain.

→ Look at the shape:
- Left whisker goes from 38 to 72 → long left tail
- Right whisker goes from 96 to 102 → short right tail
→ This suggests the distribution is skewed left (more low scores pulling the mean down).

→ In a left-skewed distribution, the mean is usually less than the median.

✔ Answer: Below the median, because there are some very low scores (like 38) that pull the average down, while most scores are higher.

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Second Plot: Average Minutes Per Night Spent On Homework (Sophomores)

Plot shows:
- Minimum = 0
- Q1 = 20
- Median = 48
- Q3 = 60
- Maximum = 190

Note: There’s an outlier at 190 (far right dot).

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

→ 60 is Q3 (third quartile).
→ By definition, 25% of data is above Q3.

✔ Answer: 25%

*(Note: Even with the outlier at 190, it’s still part of the top 25%. Box plots include outliers in the upper/lower tails unless specified otherwise.)*

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

→ Middle 50% = interquartile range (IQR) = Q3 – Q1
→ Q3 = 60, Q1 = 20
→ IQR = 60 – 20 = 40 minutes

But the question asks for the *range of times*, meaning the interval: from Q1 to Q3.

✔ Answer: From 20 to 60 minutes

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Question 9: What percent of the sophomores spend less than 20 minutes per night on homework?

→ 20 is Q1 (first quartile).
→ 25% of data is below Q1.

✔ Answer: 25%

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Final Answer:

1. 102
2. 75%
3. 88
4. 25%
5. No, because the median score was 88, which means half the class scored 88 or higher. Most students did well, though a few had lower scores.
6. Below the median, because there are some very low scores (like 38) that pull the average down, while most scores are higher.
7. 25%
8. From 20 to 60 minutes
9. 25%