Some data are used to create a box plot shown - HSC - SSCE Mathematics Standard - Question 15 - 2024 - Paper 1

To analyze which histogram is not possible based on the box plot, we need to consider the following:

1. Understanding the Box Plot: The box plot provides information about the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. From the box plot:

   • The median splits the data into two equal halves.
   • The interquartile range (IQR) is Q3 - Q1, which helps in understanding the spread of the middle 50% of the data.

2. Analyzing the Histograms: For each histogram (A, B, C, D), check whether the distribution reflected in the histogram aligns with the characteristics from the box plot. Important points to consider include:

   • The height of each bar in the histogram should reflect the data distribution, respecting the quartiles.
   • None of the bins should have a frequency distribution suggesting values outside the box plot's range.

3. Identifying the Incorrect Histogram: Once you analyze the bar heights and their distribution, identify which histogram does not conform to the data characteristics indicated by the box plot.

From the marking scheme, it is confirmed that the answer is D as it does not align with the data distributions suggested by the box plot.