Statistics - Field Sampling: Principles and Practices in Environmental Analysis - page 151

This number is found by rounding up.
The median for these same data is also 292 ppm. This is obtained by adding the central
two numbers (i.e., 286 and 298) and dividing by 2.
Carrying out the same calculation for B4, the mean is found to be 909 ppm
(rounded up). Even though the means are different from those for A4 they do not provide
enough information to tell if the two areas have different amounts of TPH or not. For this
determination calculation of the standard deviation, shown below, is needed.
The average pHs given in the next to bottom row of Table 6.3 were also obtained in
this way. In this case each of the pHs shown was obtained by finding the mean of the
three determinations of the pH of the soil core shown in the column above it [3].

6.6. STANDARD DEVIATION

The first step in determining if the two average TPH levels or the average pHs calculated
above are different or not is to first calculate the sample variance s 2 and the standard
deviation s . The first step in this process is to determine how far away from the mean
each of the data points is. To obtain this information each data point is subtracted from
the mean. From above the mean and

273-292=−19 286-292=−6 298-292=6 310−292=18

Because this gives us a mixture of positive and negative numbers the mean of these
numbers is either 0 or very close to 0, and thus gives little information about the
variability. * To make the calculation more meaningful the differences are squared, which
makes all the numbers positive. Thus

(−19) 2 =361 (−6) 2 =36 6 2 =36 18 2 =324

A more useful mean is then determined for these squared numbers:

* If no rounding is used in determining the mean, the sum of the deviations from the mean will be
0.
† The letter Σ is used to represent a summation. It tells us that the group of numbers represented by
are added together. The subscript i indicates that there are several different numbers. In
this case the first number, 273, is substituted for x i and the calculation is carried out. The second
number is then similarly taken, then the third, until all the numbers have been substituted for x i and