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True or False: Chebyshev’s Inequality applies to all distributions regardless of shape, but the Empirical Rule holds only for distributions that are bell shaped.
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3. Describing Data Numerically
Percentiles & Quartiles
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In a class rank context, what does it mean if a student is in the first quartile (Q1) of the class?
A
The student ranks exactly at the median of the class (50th percentile).
B
The student ranks in the top 25% of the class (above about 75% of classmates).
C
The student ranks in the top 75% of the class (above about 25% of classmates).
D
The student ranks in the bottom 25% of the class (below about 75% of classmates).
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Understand that quartiles divide a data set into four equal parts, each representing 25% of the data.
The first quartile (Q1) corresponds to the 25th percentile, meaning 25% of the data falls below this value.
In the context of class rank, being in the first quartile means the student is ranked at or below the 25th percentile.
This implies the student is in the bottom 25% of the class, meaning about 75% of classmates have a higher rank.
Therefore, the student is not at the median (50th percentile) nor in the top 25% or top 75%, but rather in the lowest 25% of the class.
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