Calculate the mean, median, and mode for the data.

Mean = Sum of X values / N (Number of values)

Mean = 885 /

Mean = 68.0769

Median = 62 found by arranging the numbers in ascending order and selecting the value in the (n + 1) / 2 position which is the 7th position or

56, 56, 62, 62, 62, 62, 62, 70, 75, 75, 75, 81, 87

Mode = 62 found by selecting the most frequently occurring value

Prepare a frequency distribution for the data.

Rank

Occurrences

Calculate the standard deviation for this data.

Standard Deviation = sqrt (sum (value - mean) 2) / N)

Standard Deviation = 9.78487

Explain why statisticians typically use the standard deviation rather than the average deviation.

The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data (Niles). When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you there is a relatively large standard deviation (Niles).

The average deviation is the absolute value of the difference from the mean for each data value, summed, then divided by the number of values. Therefore, the average deviation, like the standard deviation is the measure or spread of all values in a series of observations. However, the mean deviation, unlike the standard deviation, does not square the distance from the mean, so it is less affected by extreme values than the standard deviation. Thus, the standard deviation is a better measure of variability and is more frequently used for this reason. Also, the use of the absolute value in the average deviation makes calculations more complicated than the standard deviation because many statistical techniques rely on minimizing the sum of square residuals rather than the sum of absolute residuals (Mean deviation).

Bibliography

Mean deviation. http://mathworld.wolfram.com/MeanDeviation.html

Niles, R. Standard deviation. http://www.robertniles.com/stats/stdev.shtml