Analytical chemistry report

1. STATISTICAL TREATMENT OF DATA IN
DETERMINATION OF WEIGHT VARIATIONS
IN COINS
EXPERIMENT #3
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GROUP 5:
Alvarez, Karen
Garcia, Jakielou A
Pasco, Jaira Grace M.
BSED 2A

2. ABSTRACT
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• Utilized the statistical concepts in the weight variations of one-
peso PH coin using an analytical balance
• Ten one-peso coins used in this experiment with varied
production years for Set A and Set B
• Weight of the coins for Set A and Set B calculated for the
statistical parameters such as mean, median, average deviation,
standard deviation, relative standard deviation (in ppt), range,
relative range in parts per thousand (in ppt), pooled standard
deviation and confidence limit of 95%
• Mean weight of the coins: 5.98 g for Set A and 5.99 g for Set B
• Median weight of the coins: both 5.99 g for Set A and B
• Average deviation: 0.025 for Set A and 0.02 for Set B
• Standard deviation: 0.037 for Set A and 0.031 for Set B

3. ABSTRACT
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• Relative standard deviation (in ppt): 6.19 ppt and 5.18
ppt for Set A and B, respectively
• Range of weight variation: 0.11 g for Set A and 0.09 g
for Set B
• Relative range (in ppt): 18.39 ppt for Set A and 15.03
ppt for Set B
• Pooled standard deviation: 0.033 for both sets
• Q-test:
• The statistical parameters and methods used in this
experiment provide a reliable and accurate means of
analyzing and interpreting the data, which can be used
for quality control and other applications.

4. INTRODUCTION
The arithmetic mean is the sum of the measured
values divided by n, the number of measurements:
The standard deviation, s, measures how closely
the data are clustered about the mean.
The standard deviation expressed as a percentage
of the mean value is called the coefficient of
variation:
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5. INTRODUCTION
Relative standard deviation is calculated by
dividing the standard deviation by the mean value
of the data set:
From a limited number of measurements (n), one
cannot produce a true value of the representative
value; rather the population is approximated using
a confidence interval:
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6. INTRODUCTION
The range, (w) is a measure of precision; is the
difference of the highest and lowest values in a data
set.
The Q test is a simple, widely used statistical test
for deciding whether a suspected result, an outlier,
should be retained or rejected (Skoog et al., 2013):
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7. METHODOLOGY
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Check zero point each time before
using the balance
Designate data set A coins 1-6 and
data set B coins 1-10
Determine the weights of each coin
in the analytical balance
Record the weights of the 10 coins
Make sure the lever is in arrest
position and returned knobs to 0

8. Table 1. Weight of each coin in the analytical balance.
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SET A
Coin 1 6.03 g
Coin 2 5.92 g
Coin 3 5.98 g
Coin 4 6.00 g
Coin 5 5.99 g
Coin 6 5.97 g

9. Table 2. Weight of each coin in the analytical balance.
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SET B
Coin 1 6.04 g
Coin 2 5.99 g
Coin 3 5.99 g
Coin 4 6.02 g
Coin 5 5.98 g
Coin 6 5.95 g
Coin 7 5.97 g
Coin 8 5.95 g
Coin 9 5.99 g
Coin 10 6.00 g

10. Table 3. Data for statistical parameters for Set A and B.
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HIGHEST LOWEST
SET A -0.27 0.45
SET B -0.22 0.22

11. Table 3. Data for statistical parameters for Set A and B.
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STATISTICAL
PARAMETERS
SET A SET B
MEAN 5.98 5.99
MEDIAN 5.99 5.99
AVERAGE DEVIATION 0.025 0.02
STANDARD DEVIATION 0.037 0.031
RELATIVE STANDARD
DEVIATION (in ppt)
6.19 ppt 5.18 ppt
RANGE 0.11 0.09
RELATIVE RANGE in ppt 18.39 ppt 15.03 ppt
POOLED STANDARD
DEVIATION
0.033
CONFIDENCE LIMITS
(95% confidence level)
5.98 ± 0.043 5.99 ± 0.446

12. SUMMARY & CONCLUSION
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• The results of the experiment indicated that
• Q test: the results indicated that both of the sets have and no
significant outliers suggesting that some data are reliable and
can be used for further analysis

13. Q-test
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14. MEAN
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15. MEDIAN
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5.92 5.97 5.98 5.99 6.00 6.03
5.95 5.95 5.97 5.98 5.99 5.99 5.99 6.00 6.02 6.04

16. AVERAGE DEVIATION
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17. STANDARD DEVIATION
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18. STANDARD DEVIATION
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19. RELATIVE STANDARD DEVIATION (in ppt)
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20. RANGE
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21. RELATIVE RANGE (in ppt)
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22. POOLED STANDARD DEVIATION
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23. CONFIDENCE LIMITS (95% confidence level)
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24. CONFIDENCE LIMITS (95% confidence level)
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