Questions: Test Scores Find the percentile rank for each test score in the data set. Round to the nearest whole percentile. 18,28,38,43,46,49,50 The percentile rank for the value 18 is .

Test Scores Find the percentile rank for each test score in the data set. Round to the nearest whole percentile.
18,28,38,43,46,49,50
The percentile rank for the value 18 is .

Transcript text: Test Scores Find the percentile rank for each test score in the data set. Round to the nearest whole percentile. \[ 18,28,38,43,46,49,50 \] The percentile rank for the value 18 is $\square$ .

Solution

Solution Steps

Step 1: Calculate Scores Below and Equal to 18

To determine the percentile rank for the score $ 18 $ in the dataset $ \{18, 28, 38, 43, 46, 49, 50\} $, we first count the number of scores below $ 18 $ and the number of scores equal to $ 18 $.

Scores below $ 18 $: $ 0 $
Scores equal to $ 18 $: $ 1 $

Step 2: Total Number of Scores

Next, we calculate the total number of scores in the dataset, which is $ 7 $.

Step 3: Calculate Percentile Rank

Using the formula for percentile rank:

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

Substituting the values we found:

\[ \text{Percentile Rank} = \left( \frac{0 + 0.5 \times 1}{7} \right) \times 100 = \left( \frac{0.5}{7} \right) \times 100 \approx 7.142857 \]

Rounding to the nearest whole percentile gives us $ 7 $.