Given the following data, find the weight that represents the 42nd percentile.
Weights of Newborn Babies
8.3 6.5 6.0 5.4 6.7
6.5 8.1 9.2 6.4 8.0
6.8 9.0 8.7 9.3 8.0
To find the weight that represents the 42nd percentile, we need to first sort the data in ascending order:
5.4, 6.0, 6.4, 6.5, 6.5, 6.7, 6.8, 8.0, 8.0, 8.1, 8.3, 8.7, 9.0, 9.2, 9.3
Next, calculate the index for the 42nd percentile:
n = 15 (total number of data points)
P = 42nd percentile
Index = (P/100) * n
Index = (42/100) * 15
Index = 0.42 * 15
Index = 6.3
Since the index falls between the 6th and 7th data points, we will take the average of the weights at those positions:
Weight at 6th position = 6.7
Weight at 7th position = 6.8
Average weight = (6.7 + 6.8) / 2
Average weight = 6.75
Therefore, the weight that represents the 42nd percentile is 6.75.