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

To determine which histogram is not possible for the given box plot, we first analyze the box plot itself.

A box plot provides valuable information: it displays the median, quartiles, and potential outliers of the data set.

1. Identify the Key Values from the Box Plot:

   • Minimum Value: The lowest data value.
   • First Quartile (Q1): The median of the lower half of the data.
   • Median (Q2): The middle value of the data.
   • Third Quartile (Q3): The median of the upper half of the data.
   • Maximum Value: The highest data value.

2. Examine Each Histogram: Compare the bars in each histogram with the box plot's quartile values:

   • Histogram A: Check if the distribution aligns with the quartile values.
   • Histogram B: Similarly, verify the quartile distribution.
   • Histogram C: Ensure consistency with the median and quartile interpretation.
   • Histogram D: Assess this histogram closely.

3. Conclusion: Upon evaluation, Histogram D fails to represent the constraints set by the box plot, indicating why it is not a valid option.