Question
Given the following data, find the diameter that represents the 53rd percentile.
Diameters of Golf Balls
1.64 1.59 1.30 1.51 1.41
1.64 1.59 1.47 1.61 1.68
1.56 1.32 1.64 1.41 1.49
Diameters of Golf Balls
1.64 1.59 1.30 1.51 1.41
1.64 1.59 1.47 1.61 1.68
1.56 1.32 1.64 1.41 1.49
Answers
GPT 3.5
To find the diameter that represents the 53rd percentile, we need to first arrange the diameters in ascending order:
1.30 1.32 1.41 1.41 1.47
1.49 1.51 1.56 1.59 1.59
1.61 1.64 1.64 1.68
The total number of data points is 14. To find the index of the data value at the 53rd percentile, we use the formula:
Index = (percentile/100) * (n + 1)
Index = (53/100) * (14 + 1)
Index = 0.53 * 15
Index = 7.95
The index falls between the 7th and 8th data points (1.56 and 1.59). To find the value at the 53rd percentile, we can calculate the average of the 7th and 8th data points:
(1.56 + 1.59) / 2 = 1.575
Therefore, the diameter that represents the 53rd percentile is 1.575.
1.30 1.32 1.41 1.41 1.47
1.49 1.51 1.56 1.59 1.59
1.61 1.64 1.64 1.68
The total number of data points is 14. To find the index of the data value at the 53rd percentile, we use the formula:
Index = (percentile/100) * (n + 1)
Index = (53/100) * (14 + 1)
Index = 0.53 * 15
Index = 7.95
The index falls between the 7th and 8th data points (1.56 and 1.59). To find the value at the 53rd percentile, we can calculate the average of the 7th and 8th data points:
(1.56 + 1.59) / 2 = 1.575
Therefore, the diameter that represents the 53rd percentile is 1.575.