Given the following data, find the weight that represents the 24th percentile.
Weights of Newborn Babies
5.6 9.2 9.4 8.6 5.5
5.9 6.6 8.0 7.0 7.0
7.3 6.7 5.6 8.2 5.7
To find the weight that represents the 24th percentile, we first need to organize the data in ascending order:
5.5, 5.6, 5.6, 5.7, 5.9, 6.6, 6.7, 7.0, 7.0, 7.3, 8.0, 8.2, 8.6, 9.2, 9.4
There are a total of 15 data points. The formula to find the percentile rank is:
Percentile Rank = (P/100) * (n+1)
where P is the desired percentile (24 in this case), and n is the total number of data points (15 in this case).
Percentile Rank = (24/100) * (15+1) = 0.24 * 16 = 3.84
Since the percentile rank falls between the 3rd and 4th data points, we take the weighted average of the 3rd and 4th data points.
Weight at the 3rd position = 5.6
Weight at the 4th position = 5.7
Weight representing the 24th percentile = 5.6 + 0.24 * (5.7 - 5.6) = 5.6 + 0.24 * 0.1 = 5.6 + 0.024 = 5.624
Therefore, the weight that represents the 24th percentile is 5.624.