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Percent deviation quantifies how far individual data points stray from the average value of a dataset. It is a key indicator of variability and helps assess the precision of measurements.
Start by finding the mean (average) of your data set. Add all the values together and divide by the number of observations. For example, if you weigh four melons at 2 lb, 5 lb, 6 lb, and 7 lb, the sum is 20 lb. Dividing by four gives a mean weight of 5 lb.
The average deviation is the mean absolute difference between each data point and the overall mean. For each point, calculate the absolute value of its difference from the mean: D = |d – m|. Using the melon example:
Summing these deviations (3 lb + 0 lb + 1 lb + 2 lb = 6 lb) and dividing by four observations yields an average deviation of 1.5 lb.
Divide the average deviation by the mean and multiply by 100 to express it as a percentage:
Percent deviation = (1.5 lb / 5 lb) × 100 = 30 %
This means that, on average, each melon’s weight differs from the mean by 30 % of the mean weight.
When comparing experimental results to a theoretical or known value, percent deviation measures how far the experimental mean deviates from that standard. Use the formula:
Percent deviation = (Experimental – Known) / Known × 100
Example: An experiment yields a mean density of 2,500 kg/m² for aluminum, while the accepted density is 2,700 kg/m². The calculation is:
(2,500 – 2,700) / 2,700 × 100 = -7.41 %
A negative result indicates the experimental mean is lower than the standard; a positive value indicates it is higher.
