To be considered for pilot school, 12 students took a spatial reasoning test that resulted in this list of scores. Find the percentile for the score value 117.

Question

152 121 130 143 122 101 137 98 138 127 145 117 (1 point)

a. 17th percentile
b. 25th percentile
c. 77th percentile
d. 83rd percentile

Answer 1

To find the percentile for the score of 117, we need to determine how many students scored less than 117 out of the total 12 students.

First, let's arrange the scores in ascending order:

98, 101, 117, 121, 122, 127, 130, 137, 138, 143, 145, 152

Now, count the number of scores less than 117:

• Scores less than 117 are: 98, 101

There are 2 scores less than 117.

Next, we can calculate the percentile using the formula:

\[ P = \left(\frac{N_L}{N}\right) \times 100 \]

where:

• \(N_L\) is the number of values less than the score,
• \(N\) is the total number of values.

In this case:

• \(N_L = 2\)
• \(N = 12\)

Now plug in the values:

\[ P = \left(\frac{2}{12}\right) \times 100 \approx 16.67 \]

Thus, the percentile rank for a score of 117 is approximately 16.67, which would round to the 17th percentile.

Therefore, the answer is:

a. 17th percentile

Answer 2

To be considered for pilot school, 12 students took a spatial reasoning test that resulted in this list of scores. Find the value of the 90th percentile.
152 121 130 143 122 101 137 98 138 127 145 117 (1 point)

a. 101
b. 145
c. 143
d. 11

Answer 3

To find the 90th percentile of the given scores, we first need to arrange the scores in ascending order and then determine the position of the 90th percentile in the sorted list.

Step 1: Arrange the scores in ascending order:

The scores are: 98, 101, 117, 121, 122, 127, 130, 137, 138, 143, 145, 152

Step 2: Calculate the position of the 90th percentile:

The formula for finding the position \( P \) of the \( k \)th percentile in a dataset with \( N \) values is:

\[ P = \frac{k}{100} \times N \]

In this case, \( k = 90 \) and \( N = 12 \):

\[ P = \frac{90}{100} \times 12 = 10.8 \]

Since the position is not a whole number, we round it up to the next whole number, which gives us position 11.

Step 3: Find the value at position 11 in the ordered list:

The ordered list is:

1. 98
2. 101
3. 117
4. 121
5. 122
6. 127
7. 130
8. 137
9. 138
10. 143
11. 145
12. 152

The value at position 11 is 145.

Therefore, the value of the 90th percentile is:

b. 145