Question

below are 36 sorted ages of an acting award winner. find p 80 using the method presented in the textbook. 17 19 23 24 26 26 27 27 27 32 32 33 35 37 37 43 46 46 49 53 54 61 62 64 64 64 66 70 72 78 79 79 80 86 ...

Explanation:

Step1: Find the position of \( P_{80} \)

The formula for the position of the \( p \)-th percentile is \( i = \frac{p}{100} \times n \), where \( n \) is the number of data points. Here, \( p = 80 \) and \( n = 36 \). So, \( i=\frac{80}{100}\times36 = 28.8 \).

Step2: Determine the value of \( P_{80} \)

Since \( i = 28.8 \) is not an integer, we round up to the next integer, which is \( 29 \). Now, we look at the 29th data point in the sorted list. Let's list out the sorted data (we can count the positions):

1:17, 2:19, 3:23, 4:24, 5:26, 6:26, 7:27, 8:27, 9:27, 10:32, 11:32, 12:33, 13:35, 14:37, 15:37, 16:43, 17:46, 18:46, 19:49, 20:53, 21:54, 22:61, 23:62, 24:64, 25:64, 26:66, 27:70, 28:72, 29:78, 30:79, 31:79, 32:80, 33:86 (Wait, maybe I miscounted earlier. Let's do it properly. Let's list all 36 data points:

Row 1: 17, 19, 23, 24, 26, 26

Row 2: 27, 27, 27, 32, 32, 33

Row 3: 35, 37, 37, 43, 46, 46

Row 4: 49, 53, 54, 61, 62, 64

Row 5: 64, 66, 70, 72, 78, 79

Row 6: 79, 80, 86 (Wait, no, the original data as per the image: Let's count again. The data is:

17, 19, 23, 24, 26, 26,

27, 27, 27, 32, 32, 33,

35, 37, 37, 43, 46, 46,

49, 53, 54, 61, 62, 64,

64, 66, 70, 72, 78, 79,

79, 80, 86? Wait, no, the number of data points should be 36. Let's count the elements:

First column: 17,19,23,24,26,26,27,27,27,32,32,33,35,37,37,43,46,46,49,53,54,61,62,64,64,66,70,72,78,79,79,80,86? No, that's 33. Wait, the original image has:

First row (left to right): 17, 32, 49, 70

Second row:19,32,53,[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]

Answer:

Step1: Find the position of \( P_{80} \)

The formula for the position of the \( p \)-th percentile is \( i = \frac{p}{100} \times n \), where \( n \) is the number of data points. Here, \( p = 80 \) and \( n = 36 \). So, \( i=\frac{80}{100}\times36 = 28.8 \).

Step2: Determine the value of \( P_{80} \)

Since \( i = 28.8 \) is not an integer, we round up to the next integer, which is \( 29 \). Now, we look at the 29th data point in the sorted list. Let's list out the sorted data (we can count the positions):

1:17, 2:19, 3:23, 4:24, 5:26, 6:26, 7:27, 8:27, 9:27, 10:32, 11:32, 12:33, 13:35, 14:37, 15:37, 16:43, 17:46, 18:46, 19:49, 20:53, 21:54, 22:61, 23:62, 24:64, 25:64, 26:66, 27:70, 28:72, 29:78, 30:79, 31:79, 32:80, 33:86 (Wait, maybe I miscounted earlier. Let's do it properly. Let's list all 36 data points:

Row 1: 17, 19, 23, 24, 26, 26

Row 2: 27, 27, 27, 32, 32, 33

Row 3: 35, 37, 37, 43, 46, 46

Row 4: 49, 53, 54, 61, 62, 64

Row 5: 64, 66, 70, 72, 78, 79

Row 6: 79, 80, 86 (Wait, no, the original data as per the image: Let's count again. The data is:

17, 19, 23, 24, 26, 26,

27, 27, 27, 32, 32, 33,

35, 37, 37, 43, 46, 46,

49, 53, 54, 61, 62, 64,

64, 66, 70, 72, 78, 79,

79, 80, 86? Wait, no, the number of data points should be 36. Let's count the elements:

First column: 17,19,23,24,26,26,27,27,27,32,32,33,35,37,37,43,46,46,49,53,54,61,62,64,64,66,70,72,78,79,79,80,86? No, that's 33. Wait, the original image has:

First row (left to right): 17, 32, 49, 70

Second row:19,32,53,[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]