# Average Example 1

Problem  Find the average, and average deviation for the following data on the length of a pen, L.  We have 5 measurements,
(12.2, 12.5, 11.9,12.3, 12.2) cm.

 Length (cm) | 12.2 0.02 0.0004 12.5 0.28 0.0784 11.9 0.32 0.1024 12.3 0.08 0.0064 12.2 0.02 0.0004 Sum     61.1 Sum   0.72 Sum   0.1880 Average   61.1/5 = 12.22 Average   0.14

To get the average sum the values and divide by the number of measurements.
To get the average deviation,

1. Find the deviations, the absolute values of the quantity (value minus the average), |L - Lave|
2. Sum the absolute deviations,
3. Get the average absolute deviation by dividing by the number of measurements
To get the standard deviation
1. Find the deviations and square them
2. Sum the squares
3. Divide by (N-1), the number of measurements minus 1 (here it is 4)
4. Take the square root.

# Average Example 2

Problem: Find the average and the average deviation of the following measurements of a mass.

(4.32, 4.35, 4.31, 4.36, 4.37, 4.34) grams.

 Mass (grams) 4.32 0.0217 0.000471 4.35 0.0083 0.000069 4.31 0.0317 0.001005 4.36 0.0183 0.000335 4.37 0.0283 0.000801 4.34 0.0017 0.000003 Sum    26.05 0.1100 0.002684 Average     4.3417 Average   0.022

The same rules as Example 1 are applied. This time there are N = 6 measurements, so for the standard deviation we divide by (N-1) = 5.