Question

use the percentiles flow chart interactive to answer the following question. when finding the 35th percentile from a sample of 200 iq scores, the locator l is found to be 70. what is the value of the 35th percentile? choose the correct answer below: a. the 70th iq score in the sorted list b. the 35th iq score in the sorted list c. the iq score that is midway between the 70th and 71st scores in the sorted list d. the iq score that is midway between the 35th and 36th scores in the sorted list

Explanation:

To find the \( p \)-th percentile (here \( p = 35 \)) of a sample with \( n = 200 \) observations, we use the locator formula \( L=\frac{p}{100}\times n \). For \( p = 35 \) and \( n = 200 \), we calculate \( L=\frac{35}{100}\times200 = 70 \).

When the locator \( L \) is an integer, the \( p \)-th percentile is the average (midway) of the \( L \)-th and \( (L + 1) \)-th values in the sorted list. Here, \( L = 70 \), so we need the value midway between the 70th and 71st scores in the sorted list of IQ scores.

• Option A is incorrect because the 70th score alone is not the 35th percentile when \( L \) is an integer (we need the average of the 70th and 71st).
• Option B is incorrect because the 35th score is not related to the locator value of 70 (the locator calculation gives \( L = 70 \) for the 35th percentile in a sample of 200).
• Option D is incorrect because we need the midway between the 70th and 71st, not the 35th and 36th.

Answer:

C. The IQ score that is midway between the 70th and 71st scores in the sorted list