the counts will equal the square root of the
average count or mean.
One standard deviation equals 68% of the
population of events for a series.
Put these all together and:
+ 1 Std Dev =
This finding can be put to good use in evaluating tester
performance if we use it to inspect a series of counts
taken in the standard count mode.
(The procedure may also be used to evaluate any series
of nuclear tester counts. It is only necessary that the
tester not be moved during the series of counts. Counts
could be taken in any operating position, with another
tester nearby, etc.).
Two evaluation methods will be described.
One uses a hand calculator with statistic functions, the
other uses a manual checkoff method. Both techniques
work well. Both should be used with ten successive
counts taken in the 1/4 minute time period. (This will not
work if counts are taken in other time periods due to the
averaging or normalizing of the tester on long time
Enter the series of numbers into the calculator following
calculator instructions for standard deviation. Determine
the deviation and place it in one of the calculators
Pull up the mean of the series of counts and determine
the square root of the mean.
Divide the deviation by the square root.
From the above discussion, if the series was "perfect",
the square root would equal the deviation and the
division would be "1.0". The series will seldom work out
perfectly, however, and some variance from 1.0 will be
observed. It is normal for this to lie between 0.75 and
1.25 with a general tendency towards 1.0 for a normal
1-11. MANUAL EVALUATION
Take the same series of ten numbers. Use 1/4 minute
If the standard deviation of the series is to lie within
average and this is to include 68% of the series,
then this is merely stating that 68% of the numbers
should lie within
of the average or mean and that
32% should be outside the average or mean.
That is, out of a series of ten numbers, 32% or about 3
out of 10 will lie outside plus or minus the square root of
We simply add up a series of numbers, average them,
determine the square root of the average and then add
and subtract this square root to the average.
The resultant high and low limits will include 68% of the
numbers in the series and 32% will be higher or lower
than the limits.
The following example illustrates a typical tester placed
in Standard Count configuration and using the Student
Field Data Worksheet (DA Form 5448R (Moisture and
Density Tester Field Data Worksheet)), Figure 1-3, to
accumulate the data for ten counts. DA Form 5448-R is
located at the back of this TM for local reproduction
authority. This tester was normal in all respects.
We seldom are fortunate enough to have the series work
out exactly 3 out of 10 each time we run a series.
However, if we make an intelligent allowance for
variations in numbers we will observe that the series will
exhibit a general trend towards 3 out of 10. An
occasional 2 out of 10 will be observed and an
occasional 4 out of 10 will be observed. However, the
statistic probability of a 5 out of 10 or a 1 out of 10 is very
slim, and such splits should be very rare for a normal
It is important to observe the average from one such
Standard Count Evaluation to another. If the average is
within approximately 1/3 to 112 of the square root of the
prior average, then the difference between the two series