Questions: The data show the population (in thousands) for a recent year of a sample of cities in South Carolina. 19 19 25 19 69 25 28 12 25 28 14 34 92 16 13 10 19 27 112 40 22 44 115 37 38 53

The data show the population (in thousands) for a recent year of a sample of cities in South Carolina.

19 19 25 19 69 25
28 12 25 28 14 34
92 16 13 10 19 27
112 40 22 44 115 37
38 53

Transcript text: The data show the population (in thousands) for a recent year of a sample of cities in South Carolina. \begin{tabular}{llllll} 19 & 19 & 25 & 19 & 69 & 25 \\ 28 & 12 & 25 & 28 & 14 & 34 \\ 92 & 16 & 13 & 10 & 19 & 27 \\ 112 & 40 & 22 & 44 & 115 & 37 \\ 38 & 53 & & & & \end{tabular}

Solution

Solution Steps

Step 1: Sort the Data

The given population data for the cities in South Carolina is:

\[ \{19, 19, 25, 19, 69, 25, 28, 12, 25, 28, 14, 34, 92, 16, 13, 10, 19, 27, 112, 40, 22, 44, 115, 37, 38, 53\} \]

After sorting the data, we obtain:

\[ \{10, 12, 13, 14, 16, 19, 19, 19, 19, 22, 25, 25, 25, 27, 28, 28, 34, 37, 38, 40, 44, 53, 69, 92, 112, 115\} \]

Step 2: Count Values Below and Equal to 27

Next, we count the number of values below \(27\) and the number of values equal to \(27\):

Number of values below \(27\): \(14\)
Number of values equal to \(27\): \(1\)

Step 3: Calculate Total Number of Values

The total number of values in the dataset is:

\[ N = 26 \]

Step 4: Calculate the Percentile Rank

Using the formula for the percentile rank:

\[ \text{Percentile Rank} = \left( \frac{\text{Number of values below } 27 + 0.5 \times \text{Number of values equal to } 27}{\text{Total number of values}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentile Rank} = \left( \frac{14 + 0.5 \times 1}{26} \right) \times 100 = \left( \frac{14.5}{26} \right) \times 100 \approx 55.77 \]