Question

when a national sample of heights of kindergarten children was taken, a student was told that he was in the 60th percentile. explain what that means.

choose the correct interpretation below.

a. he is taller than 40 percent of all kindergarten children.
b. he is shorter than 60 percent of all kindergarten children.
c. he is taller than 60 percent of all kindergarten children.
d. he is taller than 60 kindergarten children.

Explanation:

Define the concept of percentiles

Using the Percentiles knowledge point
A percentile is a measure indicating the value below which a given percentage of observations in a group of observations falls. Specifically, the \(k\)-th percentile is the value such that at least \(k\) percent of the observations are less than or equal to it.

Apply the definition to the given scenario

Using the Percentiles knowledge point
The student is in the 60th percentile for height. This means that approximately 60% of all kindergarten children in the sample are shorter than him, or equivalently, he is taller than 60% of all kindergarten children.

Evaluate the given options

Using the Percentiles knowledge point

• (A) "He is taller than 40 percent of all kindergarten children" is incorrect because 60% are shorter than him.
• (B) "He is shorter than 60 percent of all kindergarten children" is incorrect because 60% are shorter than him, meaning he is in the top 40%.
• (C) "He is taller than 60 percent of all kindergarten children" matches the definition.
• (D) "He is taller than 60 kindergarten children" is incorrect because percentiles refer to percentages, not absolute counts.

Answer:

• (A) He is taller than 40 percent of all kindergarten children.
• (B) He is shorter than 60 percent of all kindergarten children.
• (C) He is taller than 60 percent of all kindergarten children. (Correct answer)
• (D) He is taller than 60 kindergarten children.