To create a dataset of seven data points with the given conditions:

1. Median is 10: The dataset's middle value (4th data point) should be 10.
2. IQR (Interquartile Range) forms 1 large rectangle: This implies that the 1st quartile ($Q_1$) and 3rd quartile ($Q_3$) are symmetrically spread around the median, with equal spacing between them and not divided into multiple smaller boxes.
3. Seven data points: An odd number of data points ensures a clear median.

Data Set Construction:

• We need to ensure the median (4th data point) is 10, and the quartiles are equally spaced.
• For simplicity, let the 1st quartile ($Q_1$) be 8, and the 3rd quartile ($Q_3$) be 12. This will make the IQR $Q_3 - Q_1 = 12 - 8 = 4$, giving the desired "1 large rectangle" box in the box-and-whisker plot.

A possible dataset satisfying these conditions could be:

$6, 8, 9, 10, 11, 12, 14$

• Median (4th value) = 10
• 1st Quartile ($Q_1$) = 8
• 3rd Quartile ($Q_3$) = 12
• IQR = $Q_3 - Q_1 = 4$, forming one large rectangle in the box plot.

Explanation:

• The median of 10 ensures the center value is 10.
• The quartiles (8 and 12) are symmetrically spaced around the median, so the IQR forms one large box.
• There are no outliers, and the data distribution is fairly symmetrical around the median, which supports the "1 large rectangle" box plot.

Would you like to explore further details or clarify any steps?

Related Questions:

1. What is the significance of the interquartile range (IQR) in data analysis?
2. How would the box-and-whisker plot change if we added an outlier to the dataset?
3. Can you explain how to calculate quartiles in a dataset with even numbers of points?
4. How does the box plot help in identifying skewness in a dataset?
5. What is the impact of extreme values on the median and IQR?

Tip: When constructing a box plot, remember that the IQR only accounts for the middle 50% of the data.