Answer :
Order data, find 18% position, interpolate between data points around that position. The 18th percentile diameter is about 1.435.
Sure, here are the steps to find the diameter that represents the 18th percentile, given the data in the image:
1. Order the data: First, order the data from smallest to largest. In this case, the data is already ordered as follows:
1.31, 1.32, 1.40, 1.40, 1.45, 1.50, 1.55, 1.57, 1.60, 1.62, 1.63, 1.63, 1.64, 1.64, 1.67, 1.69
2. Calculate the percentile: The 18th percentile is equal to 18% of the total number of data points. Since there are 15 data points, 18% of the data is equal to (18/100) * 15 = 2.7 data points.
3. Find the diameter at the percentile: Because the 2.7th data point doesn't fall exactly on a data point, we need to interpolate between two data points. In this case, the 2.7th data point falls between the 2nd and 3rd data points, which are 1.40 and 1.45, respectively.
4. Interpolate: To interpolate, we can use the following formula:
percentile value = lower data point + (percentile rank - position of lower data point) * (upper data point - lower data point)
In this case, the percentile value is 2.7, the lower data point is 1.40, the percentile rank is 2.7 (since we're looking for the value at the 2.7th data point), and the position of the lower data point is 2 (since it's the 2nd data point). The upper data point is 1.45.
Plugging these values into the formula, we get:
2.7 = 1.40 + (2.7 - 2) * (1.45 - 1.40)
Solving for the unknown, we get:
2.7 = 1.40 + 0.7 * 0.05
2.7 = 1.40 + 0.035
2.7 = 1.435
Therefore, the diameter that represents the 18th percentile is approximately 1.435.
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