The correct answer is option a. 25%. This means that 25% of the scores on the standardized exam lie above the third quartile.
How to determine the percentage of scores
To determine the percentage of scores on a standardized exam that lie above the third quartile, first, understand the concept of a boxplot and how it represents the distribution of data.
A boxplot, also known as a box and whisker plot, provides a visual representation of the distribution of a dataset. It includes several key components, such as the minimum and maximum values, the median (second quartile), and the first and third quartiles.
The box in the boxplot represents the interquartile range (IQR), which spans from the first quartile (Q₁) to the third quartile (Q₃). The median (Q₂) is represented by a line within the box. The whiskers extend from the box to the minimum and maximum values, excluding any outliers.
Now, to determine the percentage of scores that lie above the third quartile, we need to understand the relationship between quartiles and percentile ranks.
The first quartile (Q₁) represents the 25th percentile, meaning 25% of the scores fall below Q₁. The third quartile (Q₃) represents the 75th percentile, indicating that 75% of the scores fall below Q₃.
Since we want to determine the percentage of scores above Q₃, subtract 75% from 100%:
100% - 75% = 25%
Therefore, the correct answer is option a. 25%. This means that 25% of the scores on the standardized exam lie above the third quartile.