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Find the percentile for the data value.

Data set: 118, 130, 122, 116, 124, 126, 116, 114, 121, 118, 122, 132, 114, 118, 120, 115

Data value: 124

Answer :

Final answer:

To find the percentile of the value 124 in the dataset, it is first ordered, and the value's position is found. Then, applying the formula for percentile rank, 124 is determined to be in the 81st percentile, indicating it is greater than or equal to 81% of the dataset's values.

Explanation:

To find the percentile for the data value 124 in the given data set, first, we will order the data from smallest to largest. The ordered data set is: 114, 114, 115, 116, 116, 118, 118, 118, 120, 121, 122, 122, 124, 126, 130, 132. Next, we find the position of 124, which is 13th in the ordered list. Then, to calculate the percentile, we use the formula:

Percentile rank = (i/n) × 100

Where i is the rank order of the data value and n is the total number of data values.

In this case, i = 13 and n = 16, so the percentile rank of 124 is:

(13/16) × 100 = 81.25

Therefore, the data value 124 is in the 81st percentile of this data set. This means that 124 is greater than or equal to 81% of the values in the data set.

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