Here is a sorted data set:

\[ n = 117 \]

\[ 34.4, 37.2, 39.7, 43.9, 44, 44.7, 46.9, 48.6, 48.8, 50.1, 50.1, 51.3, 51.4, 51.4, 52.1, 52.2, 52.3, 52.4, 52.7, 53.3, 53.7, 54.1, 54.3, 54.4, 54.7, 55.3, 55.4, 55.6, 55.7, 55.7, 55.7, 56, 56, 56.8, 57, 57.3, 57.4, 57.4, 57.5, 57.5, 57.6, 57.6, 57.7, 58, 58, 58.3, 58.4, 58.5, 58.6, 58.8, 58.8, 58.9, 59, 59, 59.2, 59.7, 59.7, 59.8, 59.9, 60.3, 60.4, 60.5, 60.8, 60.8, 60.8, 61.1, 61.3, 61.4, 61.5, 61.7, 62.2, 62.6, 62.6, 63.3, 63.4, 63.6, 63.7, 63.7, 64.1, 64.1, 64.1, 64.5, 64.5, 64.6, 64.7, 65.4, 66.1, 66.4, 66.9, 66.9, 67.4, 67.5, 67.9, 68, 68.5, 68.8, 69, 69.2, 70, 70.1, 70.3, 70.4, 70.6, 71.7, 72.1, 72.6, 72.8, 72.9, 73.3, 73.9, 74.1, 76, 76.3, 77.7, 80.2 \]

Find the 56th percentile ($ P_{56} $):

The 56th percentile is the value that is greater than 56% of the data and less than 44% of the data. To find the 56th percentile, use the following steps:

Arrange the data in ascending order.
Find the 56th value in the data set.
This value is the 56th percentile.

In this case, the data is already arranged in ascending order. The 56th value in the data set is 58.5. Therefore, the 56th percentile is 58.5.

The data is arranged in ascending order as follows:

44 44.7 46.9 48.6 48.8 34.4 37.2 39.7 43.9 51.4 52.1 52.2 52.3 52.4 50.1 50.1 51.3 51.4 54.3 54.4 54.7 55.3 55.4 52.7 53.3 53.7 54.1 56 56 56.8 57 57.3 55.6 55.7 55.7 55.7 57.5 57.6 57.6 57.7 58 57.4 57.4 57.5 57.5 58.5 58.6 58.8 58.8 58.9 58 58 58.3 58.4 59.7 59.7 59.8 59.9 60.3 60.4 59 59 59.2 60.8 61.1 61.3 61.4 61.5 61.7 60.5 60.8 60.8 63.3 63.4 63.6 63.7 63.7 64.1 62.2 62.6 62.6 64.5 64.6 64.7 65.4 66.1 66.4 64.1 64.1 64.5 67.5 67.9 68 68.5 68.8 69 66.9 66.9 67.4 70.1 70.3 70.4 70.6 71.7 72.1 72.6 69.2 70 73.9 74.1 76 76.3 77.7 80.2 72.8 72.9 73.3

The 56th value in the data set is 58.5. Therefore, the 56th percentile is 58.5.

Find out more on percentile here: https://brainly.com/question/24245405

#SPJ4