To solve a box plot, we need to determine the five-number summary of the given data. This consists of:

1. Minimum: The smallest value.
2. Q1 (First Quartile): The median of the lower half of the data (excluding the overall median).
3. Median: The middle value of the dataset.
4. Q3 (Third Quartile): The median of the upper half of the data (excluding the overall median).
5. Maximum: The largest value.

Let’s start by arranging the data in ascending order:

$60, 65, 78, 85, 92, 103, 120$

Step 1: Identify the Median

Since there are 7 data points (an odd number), the median is the middle value.

$\text{Median} = 85$

Step 2: Calculate Q1 (First Quartile)

Q1 is the median of the lower half: $60, 65, 78$. Since this subset has 3 numbers, the middle value is:

$Q1 = 65$

Step 3: Calculate Q3 (Third Quartile)

Q3 is the median of the upper half: $92, 103, 120$. Similarly, the middle value is:

$Q3 = 103$

Step 4: Identify the Minimum and Maximum

• Minimum = 60
• Maximum = 120

Five-Number Summary:

• Minimum = 60
• Q1 = 65
• Median = 85
• Q3 = 103
• Maximum = 120

Box Plot Interpretation:

• The box spans from Q1 (65) to Q3 (103).
• The line inside the box is the median (85).
• Whiskers extend from the minimum (60) to the maximum (120).

Would you like more details or have any questions about how I derived these values?

Here are 5 follow-up questions for practice:

1. What is the interquartile range (IQR) for this dataset?
2. How would you identify outliers based on the IQR method?
3. How does the box plot visually represent the spread of the data?
4. What does it mean if the median is closer to Q1 or Q3 in a box plot?
5. How can we modify the dataset to create a symmetric box plot?

Tip: The interquartile range (IQR) helps identify the spread of the middle 50% of the data, making it a useful measure for detecting outliers!