Question

use the percentiles flow chart interactive to answer the following question. when finding the 37th percentile from a sample of iq scores, the locator l is found to be 45.5. what is the value of the 37th percentile? choose the correct answer below. a. the 46th iq score in the sorted list b. the 45th iq score in the sorted list c. the iq score that is midway between the 45th and 46th scores in the sorted list. d. the iq score that is midway between the 37th and 38th scores in the sorted list.

Explanation:

To find the \( p \)-th percentile, we use the locator formula \( L = \frac{p}{100}(n) \), where \( n \) is the number of observations. If \( L \) is a non - integer, we round up to the next integer, and the percentile is the value at that position. If \( L \) is a decimal (not an integer), the percentile is the average of the values at the positions \( \lfloor L
floor \) and \( \lceil L
ceil \). Here, the locator \( L = 45.5 \), which means we need to find the value midway between the 45th and 46th scores in the sorted list of IQ scores (since \( \lfloor45.5
floor=45 \) and \( \lceil45.5
ceil = 46 \)).

• Option A: The 46th score would be used if \( L\) was rounded up to 46, but since \( L = 45.5 \), we need the mid - point, not just the 46th score.
• Option B: The 45th score alone is not sufficient as \( L = 45.5 \) indicates we need to consider both the 45th and 46th scores.
• Option D: The 37th percentile has nothing to do with the 35th and 36th scores. The locator is 45.5, so we focus on the 45th and 46th scores.

Answer:

C. The IQ score that is midway between the 45th and 46th scores in the sorted list.