Answer to Question #337649 in Statistics and Probability for shimmy

Question

Lilian got a score of 55, which is equivalent to the 70th percentile in a mathematics test. Which of the following is NOT true?

A. 70% of the students got a score less than or equal to Lilian’s score.

B. Thirty percent of the class got scores of 55 and above.

C. If the passing mark is the first quartile, she passed the test.

D. Her score is below the 5th decile.

Answer 1

To prove that the statement D is incorrect, consider the value of the 5th decile and 70th decile. Decile means the score points that divide the distribution into 10 equal parts. They are often denoted by D. On the other hand, percentile is the score points which divide a distribution into one hundred equal parts, so that each part represents the data set. It is often denoted by P.

Given that Lillian's score is in the 70th percentile and comparing decile with percentile will give: 1st decile = 10th percentile. It follows that the 5th decile = 50th percentile. But Lillian's score is the 70th percentile which is greater than the 50th percentile or the 5th decile. Therefore, her score of 55 does not belong to the scores below the 5th decile.