SOLUTION: Dennis and Christine scored 32 and 23, respectively, in the National Career Assessment Examination (NCAE). The determining factor for a college scholarship is that a student's scor

Algebra ->  Probability-and-statistics -> SOLUTION: Dennis and Christine scored 32 and 23, respectively, in the National Career Assessment Examination (NCAE). The determining factor for a college scholarship is that a student's scor      Log On


   

Question 1181511: Dennis and Christine scored 32 and 23, respectively, in the National Career Assessment Examination (NCAE). The determining factor for a college scholarship is that a student's score should be in top 10% of the scores of his/her graduating class. The students in the graduating class obtained the following scores in the NCAE
Suppose that the given data is written in table
NCAE Scores f(frequency) LB 39-41 6
36-38 7
33-35 9
30-32 13
27-29 22
24-26 10
21-23 9
18-20 7
15-17 8
12-14 4
9-11 2
6-8 1
3-5 1
Question
1. Complete the table by filling the LB or the lower boundaries and 2. Find the 3rd quartile, 72nd percentile and the 8th decile of the set of data
3. What is the percentile rank of Dennis and Christine


Answer by CPhill(2264) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the solution:
**1. Completed Table:**
To find the lower boundaries (LB), subtract 0.5 from each lower class limit.
| NCAE Scores | f (frequency) | LB |
|-------------|---------------|-------|
| 39-41 | 6 | 38.5 |
| 36-38 | 7 | 35.5 |
| 33-35 | 9 | 32.5 |
| 30-32 | 13 | 29.5 |
| 27-29 | 22 | 26.5 |
| 24-26 | 10 | 23.5 |
| 21-23 | 9 | 20.5 |
| 18-20 | 7 | 17.5 |
| 15-17 | 8 | 14.5 |
| 12-14 | 4 | 11.5 |
| 9-11 | 2 | 8.5 |
| 6-8 | 1 | 5.5 |
| 3-5 | 1 | 2.5 |
**2. 3rd Quartile (Q3), 72nd Percentile (P72), and 8th Decile (D8):**
First, find the cumulative frequency (cf):
| NCAE Scores | f | cf |
|-------------|----|----|
| 39-41 | 6 | 88 |
| 36-38 | 7 | 82 |
| 33-35 | 9 | 75 |
| 30-32 | 13 | 66 |
| 27-29 | 22 | 53 |
| 24-26 | 10 | 31 |
| 21-23 | 9 | 21 |
| 18-20 | 7 | 12 |
| 15-17 | 8 | 5 |
| 12-14 | 4 | 1 |
| 9-11 | 2 | 1 |
| 6-8 | 1 | 1 |
| 3-5 | 1 | 1 |
* **Q3:** Q3 is the 75th percentile. (75/100) * 88 = 66. The 66th value falls in the 33-35 class.
Q3 = LB + [( (75/100) * N - cf_below ) / f_class ] * class_width
Q3 = 32.5 + [ (66 - 53) / 9 ] * 3
Q3 = 32.5 + 4.33 = 36.83
* **P72:** (72/100) * 88 = 63.36. The 63.36th value falls in the 30-32 class.
P72 = 29.5 + [(63.36 - 53) / 13] * 3
P72 = 29.5 + 2.41 = 31.91
* **D8:** (8/10) * 88 = 70.4. The 70.4th value falls in the 33-35 class.
D8 = 32.5 + [(70.4 - 53) / 9] * 3
D8 = 32.5 + 5.8 = 38.3
**3. Percentile Rank of Dennis and Christine:**
* **Dennis (score 32):** Dennis's score falls in the 30-32 class.
Percentile Rank = [ (cf_below + 0.5 * f_class) / N ] * 100
Percentile Rank = [ (53 + 0.5 * 13) / 88 ] * 100
Percentile Rank = [ (53 + 6.5) / 88 ] * 100
Percentile Rank = (59.5 / 88) * 100 ≈ 67.61
* **Christine (score 23):** Christine's score falls in the 21-23 class.
Percentile Rank = [ (21 + 0.5 * 9) / 88 ] * 100
Percentile Rank = [ (21 + 4.5) / 88 ] * 100
Percentile Rank = (25.5 / 88) * 100 ≈ 28.98