Question

Find the 24th percentile, P24, from the following data: 3 8 12 14 22 23 25 41 44 46 48 59 63 65 67 75 78 81 82 83 84 85 97 100 A) P24 = 24.5 B) P24 = 45.5 C) P24 = 64.5 D) P24 = 78.5

Answer 1

To find the 24th percentile of a dataset, multiply the total number of data points by 0.24. For the given dataset, P24 corresponds to the 6th value, which is 23, an option not listed in the provided choices.

Step-by-step explanation:

To find the 24th percentile, also represented as P24, from the given dataset:

3 8 12 14 22 23 25 41 44 46 48 59 63 65 67 75 78 81 82 83 84 85 97 100,

we first need to determine the position of P24 in the ordered list. To do this, we multiply the total number of data points (24 in this case) by the percentile we want to find (0.24 for the 24th percentile), which gives us:

Position = 24 * 0.24 = 5.76.

Since the position is not a whole number, we round up to the nearest whole number to find the rank of the data value that corresponds to P24. Therefore, we look at the 6th value in the ordered list.

Looking at the list, the 6th data value is 23.

Therefore, the 24th percentile (P24) is 23, which is not one of the provided options, indicating a possible error in either the dataset provided in the question or the options given for answers.

Answer 2

To find the 24th percentile, one must calculate the position as (P/100) * (N + 1). However, additional calculation shows none of the provided answer choices match the correct value, indicating a possible error in the question or answer choices.

Step-by-step explanation:

To find the 24th percentile, P24, from the given data, we need to calculate the position in the ordered dataset where 24 percent of the data lies below. First, we order the data, which is already sorted from lowest to highest in the question. To calculate the position of P24, we use the formula:

Position = (P/100) * (N + 1)

where P is the percentile (in this case, 24) and N is the number of data points (in this case, 24 since there are 24 data points in the dataset).

Calculating the position gives us:

Position = (24/100) * (24 + 1) = 6. The 6th value in the dataset is the 24th percentile, which is 23.

However, because the calculated position (6) isn’t a whole number, we take the average of the 6th and 7th data values in the sorted set:

P24 = (22 + 23)/2 = 22.5

None of the answer choices directly match this calculation, but since we should follow the convention of rounding to the nearest whole number, we'd find that none of the answer choices given (A: 24.5, B: 45.5, C: 64.5, D: 78.5) correctly represents the 24th percentile of the provided data. Hence, there might be a mistake in the question or in the provided options.