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statistically classified as not belonging to the same population and can be omitted

from subsequent calculations. Usually, it is applied to the highest and lowest values

because they are the most suspected outlier values [4].

4. 

How the statistical parameters calculated from data set 1 compare to those obtained

from data set 2.

The experimental mean obtained from the two data sets slightly differ from one

another. On Data Set 1, the experimental mean was 3.6004 while the mean for Data

Set was 3.5997. It was observed that the standard deviation obtained from Data Set

2 which was 0.0280 is lower than that of Data Set 1 which is 0.0317. This apparent

decrease of standard deviation in Data Set 2 means that the precision of the data

gathered was higher compared to Data Set 1. There was no observed change in the

Range and Relative Range between the two experimental sets. There was also

almost no change in the two sets’ confidence limits. 

5. 

The significance of pooled standard deviation

Pooled standard deviation is a method for estimating a single standard deviation

that can represent all independent samples when they are assumed to have a

common standard deviation. It is the average spread of all data points about their

group mean. It is a weighted average of each group's standard deviation. The

weighting gives larger groups a proportionally greater effect on the overall estimate.

This is used in t-tests, ANOVAs, control charts, and capability analysis [1].

6.  The 3 types of experimental error. Give examples of each type [5] [6].

a. 

Systematic errors- these errors affect the accuracy of measurement and

commonly are due to faulty calibrations and defective readings. A systematic

error in a series of replicate measurements causes all the results to be too high

or too low. These errors cannot be improved by repetitive trials.

Ex. Loss of volatile analyte while heating a sample, data obtained from a

stopwatch which is running slow.

b. 

Random errors- these affect the precision of a measurement. Random errors arestatistical fluctuations (in either direction) in the measured data due to the

precision limitations of the measurement device. Random errors can be

evaluated through statistical analysis and can be reduced by averaging over a

large number of observations.

Ex. measuring the mass of a ring three times using the same balance and get

slightly different values: 17.46 g, 17.42 g, 17.44 g

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c.  Gross errors- t his type of error occurs on the experimenter’s carelessness or lack

of skill in performing a specific method. They usually occur only occasionally, are

often large, and may cause a result to be either high or low.

Ex. Touching a weighing bottle with your fingers after its empty mass is

determined will cause a high mass reading for a solid weighed in the

contaminated bottle.

7.  The Gaussian/normal distribution and the requirements for a data set to have a

normal distribution.

It is also known as Bell Curve. Basically, the trend in this distribution is that the

middle group has the highest frequency and decreases as the group deviates from

the center. For a data set to be considered to have normal distribution, it must the

following characteristics [7]:

a.  Normal distributions are symmetric around their mean.

 b.  The mean, median, and mode of a normal distribution are equal.

c.  The area under the normal curve is equal to 1.0.

d.  Normal distributions are denser in the center and less dense in the tails.

e.  Normal distributions are defined by two parameters, the mean (μ) and the

standard deviation (σ). 

f.  68% of the area of a normal distribution is within one standard deviation of the

mean.

g.  Approximately 95% of the area of a normal distribution is within two standard

deviations of the mean

8.  The rationale behind the use of forceps/crucible tongs in handling the coins

Analytical balance is an ultra-sensitive instrument and is designed to measure

masses at 0.0002 g. In the experiment, forceps and crucibles, not bare hands, were

used to transfer objects from the balance. This is because using bare hands to

transfer objects will leave fingerprint marks that contain moisture and has the

tendency to exhibit hygroscopy[8].

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REFERENCES:

[1] Crouch, S. S; Holler F. J.; Skoog, D. A; West, D. M.; Fundamentals of Analytical Chemistry,

9th edition; Brooks/ Cole; Belmont, CA; 2014

[2] Minitab. What is Standard Deviation. http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/introductory-concepts/standard-

deviation-variance-and-the-normal-distribution/standard-dev/  (accessed September 2,

2014)

[3] What is Series. What are confidence intervals and p-values?  

http://www.medicine.ox.ac.uk/bandolier/painres/download/whatis/what_are_conf_inter.

pdf   (accessed September 2, 2014)

[4] University of Toronto. Stats Tutorial - Instrumental Analysis and Calibration.

http://www.chem.utoronto.ca/coursenotes/analsci/stats/Outliers.html (accessed

September 2, 2014) 

[5] Southeastern Louisiana University. Random Error and Systematic Error.

http://www2.southeastern.edu/Academics/Faculty/rallain/plab193/labinfo/Error_Analy

sis/05_Random_vs_Systematic.html (accessed September 2, 2014)

[6] Columbia University. Systematic Errors. 

http://phys.columbia.edu/~tutorial/rand_v_sys/tut_e_5_2.html (accessed September 2,

2014)

[7] Online Statistics Education: An Interactive Multimedia Course of Study. Introduction toNormal Distribution. http://onlinestatbook.com/2/normal_distribution/intro.html 

(accessed September 2, 2014)

[8] Science Daily. Hygroscopy. http://sciencedaily.com/articles/h/hygroscopy.htm 

(accessed September 2, 2014)