Final answer:
To estimate the 65th percentile of a data set, you must first sort the data, then calculate the position using the formula P = n + 1 percentile / 100, and if necessary, perform linear interpolation between the closest data points.
Step-by-step explanation:
To find the 65th percentile of a data set using linear interpolation, you need to first arrange the data in ascending order. In this case, the data set provided needs to be sorted: 0 -3 2 5 2 1 7. When sorted, it would look like this: -3 0 1 2 2 5 7. The 65th percentile will be a value below which 65 percent of the data falls.
After sorting the data, we calculate the position of the 65th percentile in the dataset using the formula P = n + 1 percentile / 100, where P is the position and n is the number of observations. If P is not an integer, then we must interpolate between the surrounding data points.
For example, if we were finding the 70th percentile in another dataset, and we calculated P to be 65.6 as shown in Solution 6.8, this would mean that we would take the test score that corresponds to the 65th position and then use linear interpolation to estimate the actual 70th percentile score between the 65th and the 66th data points.