Final answer:
To find the diameter that represents the 55th percentile, arrange the data in ascending order and determine the value at position (0.55)(15). The diameter that represents the 55th percentile is 1.52 cm.
Step-by-step explanation:
To find the diameter that represents the 55th percentile, we first need to arrange the data in ascending order: 1.30, 1.31, 1.32, 1.38, 1.45, 1.46, 1.47, 1.49, 1.52, 1.52, 1.54, 1.54, 1.60, 1.62, 1.69. There are 15 data points, so the 55th percentile corresponds to the value at position (0.55)(15) = 8.25, which rounds up to 9.
Therefore, the diameter that represents the 55th percentile is 1.52 cm.
To find the diameter that represents the 55th percentile of the given diameters of golf balls, we must first organize the data in ascending order. Given the distribution of diameters: 1.30, 1.31, 1.32, 1.38, 1.45, 1.46, 1.47, 1.49, 1.52, 1.52, 1.54, 1.54, 1.60, 1.62, 1.69. There are 15 observations.
Now, to find the position of the 55th percentile in our ordered data set, we multiply 55% (or 0.55) by the number of observations plus 1. The formula for finding the kth percentile Pk in an ordered data set with n observations is:
Pk = (k/100) × (n + 1)
In this case:
55th percentile: P55 = (0.55) × (15 + 1)
This yields P55 = 8.8. Since the result is not a whole number, the 55th percentile is between the 8th and 9th values in the ordered set. We'll interpolate by taking the average of these two values (1.52 and 1.54).
The diameter that represents the 55th percentile is:
(1.52 + 1.54) / 2 = 1.53
Therefore, the 55th percentile diameter of the golf balls is 1.53 cm.