Describe how you could find the 75th percentile score in a set of 20 scores.
Arrange the 20 scores in order from lowest to highest. Divide them into 4 equal groups. The 5th score from the top would be the 75th percentile score.
To find the 75th percentile score in a set of 20 scores, you first need to determine the position of the score within the dataset. Here's how you can do it:
1. Arrange the 20 scores in ascending order from smallest to largest.
2. Calculate the index of the 75th percentile using the formula: (percentile / 100) * (number of data points + 1). In this case, the percentile is 75, and the number of data points is 20.
Index = (75 / 100) * (20 + 1) = 0.75 * 21 = 15.75.
Note: Since the index is not a whole number, we will need to interpolate to find the exact position.
3. Identify the lower index value. In this example, it is 15, which corresponds to the 15th score in the ordered set.
4. Identify the upper index value. In this example, it is 16, which corresponds to the 16th score in the ordered set.
5. Use linear interpolation to calculate the exact position of the 75th percentile between the two scores:
Percentile score = lower score + (index - lower index) * (upper score - lower score).
In this case, the lower score is the 15th score, and the upper score is the 16th score.
Percentile score = score15 + (0.75 - 15) * (score16 - score15).
6. Compute the percentile score using the interpolated values obtained in Step 5.