Given the following data, find the weight that represents the 40th percentile.
Weights of Newborn Babies
8.5 7.0 8.6 8.9 6.8
7.5 9.4 8.7 6.2 6.0
9.0 5.6 8.9 5.9 6.4
To find the weight that represents the 40th percentile, first sort the weights in ascending order:
5.6, 5.9, 6.0, 6.2, 6.4, 6.8, 7.0, 7.5, 8.5, 8.6, 8.7, 8.9, 8.9, 9.0, 9.4
Next, calculate the rank of the 40th percentile: 0.4 * 15 = 6
Since the rank is not a whole number, we'll need to interpolate between the 6th and 7th data points:
Weight at the 6th position = 6.8
Weight at the 7th position = 7.0
Interpolating:
Weight at 40th percentile = 6.8 + (7.0 - 6.8) * 0.2 = 6.8 + 0.2 * 0.2 = 6.8 + 0.4 = 7.2
Therefore, the weight that represents the 40th percentile is 7.2.