How do you determine the percentile of a value when the low, lower quartile, median, mean, upper quartile, and high are known?

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To determine the percentile of a value when the low, lower quartile, median, mean, upper quartile, and high are known, you can use the following formula:

Percentile = (number of values below target value / total number of values) x 100

First, you need to calculate the total number of values in the dataset. This is just the sum of the frequencies of all the data points.

Next, identify the position of the target value in the dataset relative to the values of the low, lower quartile, median, mean, upper quartile, and high. If the target value is below the low, then the percentile is 0. If it is above the high, then the percentile is 100. If the target value falls within the range of the dataset, then you can use the formula above to calculate its percentile.

For example, if the target value is greater than the median but less than the upper quartile, then you know that it falls between the 50th and 75th percentiles. To determine the exact percentile, you can subtract the position of the upper quartile from the position of the target value, and divide by the total number of values:

Percentile = ((position of target - position of upper quartile) / total number of values) x 100

This will give you the percentile of the target value within the dataset.