The standard deviation (SD) quantifies variability. If the data follow a bell-shaped Gaussian distribution, then 68% of the values lie within one SD of the mean (on either side) and 95% of the values lie within two SD of the mean. The SD is expressed in

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The arithmetic mean is the "standard" average,
often simply called the "mean"
The standard deviation (SD) quantifies
variability. If the data follow a bell-shaped
Gaussian distribution, then 68 of the values lie
within one SD of the mean (on either side) and
95 of the values lie within two SD of the mean.
The SD is expressed in the same units as your
data.
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To apply a significance test, a hypothesis must
be clearly stated and must have a quantity with a
calculated probability associated with it. This
is the fundamental difference between a hunch and
a hypothesis testa quantity and a probability.
The hypothesis will be accepted or rejected on
the basis of a comparison of the calculated
quantity with a table of values relating to a
normal distribution. As with the confidence
interval, the analyst selects an associated level
of certainty, typically 95. The starting
hypothesis takes the form of the null
hypothesis What is a null hypothesis? The null
hypothesis is stated in such a way as to say that
there is no difference between the calculated
quantity and the expected quantity, save that
attributable to normal random error. As regards
to the outlier in question, the null hypothesis
for the chemist and the trainee states that the
11.0 value is not an outlier and that any
difference between the calculated and expected
value can be attributed to normal random error.
The P value is a probability, with a value
ranging from zero to one. If the P value is
small, you'll conclude that the difference is
unlikely to be a coincidence Plt0.05
"significant Pgt0.05, "not significant"
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t testAnother hypothesis test used in forensic
chemistry is one that compares the means of two
data sets. In the supervisortrainee example, the
two chemists are analyzing the same unknown, but
obtain different means. The t-test of means can
be used to determine whether the difference of
the means is significant. The t-value is the same
as that used in for determining confidence
intervals. This makes sense the goal of the
t-test of means is to determine whether the
spread of two sets of data overlap sufficiently
for one to concludethat they are or are not
representative of the same population.In the
supervisortrainee example, the null hypothesis
could be stated as The mean obtained by the
trainee is not significantly different than the
mean obtained by the supervisor at the 95
confidence level Stated another way, the means
are the same and any difference between them
isdue to small random errors.
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Table Bullets and fragments received by the
FBI. Specimen Description Total weight,
grains Total weight,mg CE 399 (Q1) Bullet from
stretcher (lead core plus jacket) 158.6 10,277 C
E 567 (Q2) Bullet fragment from seat cushion
(lead core plus brass jacket) 44.6 2,890 CE
569 (Q3) Bullet fragment from front seat
(jacket) 21.0 1,361 CE 843 (Q4,5) Two lead
fragments from Presidents head2 1.65
0.15 107 9.7 CE 842 (Q9) Three lead fragments
from Connallys arm 0.5 32 CE 840 (Q14) Three
lead fragments from rear carpet 0.9, 0.7,
0.7 58, 45, 45 CE 841 (Q15) Scraping from inside
surface of windshield None listed
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Table Individual determinations of antimony in
the FBIs Run 4
Specimen Weight of subfragment, mg Sb, ppm
Q1 7.16 643
4.20 636
1.79 750
1.24 749
1.16 749
15.55 70560
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Table Individual determinations of antimony in
the FBIs Run 4
Specimen Weight of subfragment, mg Sb, ppm
Q9 1.92 690
2.07 662
1.34 677
5.33 67614
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Table Individual determinations of antimony in
the FBIs Run 4
Specimen Weight of subfragment, mg Sb, ppm
Q2 39.75 521
21.60 521
3.84 578
3.68 515
68.87 53430
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Table The FBIs results for silver and antimony
in bullets and fragments  (concentrations in
ppm).