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We appreciate your visit to Given the following data find the diameter that represents the 18th percentile Diameters of golf balls 1 57 1 62 1 31 1 64 1. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Given the following data, find the diameter that represents the 18th percentile.

Diameters of golf balls:
1.57, 1.62, 1.31, 1.64, 1.40, 1.69, 1.32, 1.40, 1.60, 1.55, 1.64, 1.63, 1.50, 1.45, 1.67

Answer :

Final answer:

The 18th percentile diameter of the golf balls is slightly less than 1.40. To find the 18th percentile of the golf ball diameters, the values are first organized in ascending order. The percentile position is calculated with the formula P = (n + 1) * (percentile / 100), and then the specific value is estimated based on the position, indicating the 18th percentile is just under 1.40.

Explanation:

To find the diameter that represents the 18th percentile among the diameters of golf balls, we must first order the given data from smallest to largest. Once the data is arranged, we use the percentile formula: P = (n + 1) * (percentile / 100), where P is the position in the ordered set and n is the number of observations.

Step-by-step for finding the 18th percentile:

  1. Organize the diameters in ascending order: 1.31, 1.32, 1.40, 1.40, 1.45, 1.50, 1.55, 1.57, 1.60, 1.62, 1.63, 1.64, 1.64, 1.67, 1.69
  2. Calculate the position: P = (15 + 1) * (18 / 100) = 16 * 0.18 = 2.88. The 18th percentile lies between the 2nd and 3rd values in the ordered set.
  3. Interpolate if necessary: Since 2.88 is not a whole number, we take the 2nd value and proceed to the 3rd value in our ordered set. Our answer will be a value between 1.32 and 1.40.
  4. Since our position P is closer to 3 than to 2, we can estimate that the 18th percentile is closer to 1.40 than 1.32.

Therefore, the 18th percentile diameter of the golf balls is slightly less than 1.40.

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