Exercise 2 Page 125

Let's rearrange the scores from the least to the greatest first. 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 25, 26, 27, 28, 29. Now, we can find the performer which was at the 50^\text{th} percentile, 25^\text{th} percentile, and 75^\text{th} percentile!

50^(th) Percentile

The 50^\text{th} percentile means that 50 % of the total scores were below a given score. Therefore, to find the performer which was at the 50^\text{th} percentile, we need to determine how many scores make up 50 % of the total scores. There are 20 scores, so let's find 50 % of 20 using the percent proportion. a/b=p/100Let's do it!

We can see that 10 scores are 50 % of the total scores, let's identify them. 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 25, 26, 27, 28, 29 The score that follows the first ten is 17. Therefore, 17 is the 50^\text{th} percentile, as 50 % of the total scores are below it. From the table, we can tell that this is Arnold's score.

25^(th) Percentile

Using the same reasoning, we have to find how many scores make up 25 % of the total scores. We can also do it using the percent proportion.

We can see that 5 scores are 25 % of the total scores, let's identify them. 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 25, 26, 27, 28, 29 The score that follows the first 5 is 11. Therefore, 11 is the 25^\text{th} percentile, as 25 % of the total scores are below it. From the table, we can tell that this is Ingrid's score.

75^(th) Percentile

Now, we have to find what is the 75 % of the total scores. One more time, we can do it using the percent proportion!

We can see that 15 scores are 75 % of the total scores, let's identify them. 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 25, 26, 27, 28, 29 The score that follows the first 15 is 25. Therefore, 25 is the 75^\text{th} percentile, as 75 % of the total scores are below it. From the table, we can tell that this is Brooke's score.