# Application of Statistical Concepts in Determination of Weight Variation in Samples

**Topics:**Normal distribution, Statistics, Standard deviation

**Pages:**4 (990 words)

**Published:**February 28, 2012

APPLICATION OF STATISTICAL CONCEPTS IN THE DETERMINATION OF WEIGHT VARIATION IN SAMPLES APRIL JOY H. GARETE DEPARTMENT OF MINING, METALLURGICAL AND MATERIALS ENGINEERING, COLLEGE OF ENGINEERING UNIVERSITY OF THE PHILIPPINES, DILIMAN QUEZON CITY, PHILIPPINES RECEIVED NOVEMBER 29, 2011

RESULTS AND DISCUSSION A. Weight of Samples Sample No. 1 2 3 4 5 6 7 8 9 10 Data Set 1: Sample No. 1-6 Data Set 2: Sample no. 1-10 B. Q-Test Data Set 1 2 C. Reported Values Parameter X S RSD R RR CL Data Set 1 3.6320 + 0.0005 0.092447 25.453 0.2721 + 0.0003 74.92 + 0.08 3.63 + 0.14 Data Set 2 3.6055 + 0.0006 0.027485 7.6231 0.0902 + 0.0003 25.02 + 0.08 3.61 + 0.03 Suspect Values H: 3.8094 L: 3.5373 H: 3.8094 L: 3.5373 Qtab 0.740 0.740 0.568 0.568 Qexp 0.66850 0.20397 0.66850 0.20397 Conclusion Accepted Accepted Rejected Accepted Weight, g 3.5928 + 0.0002 3.6083 + 0.0002 3.6210 + 0.0002 3.5373 + 0.0002 3.6234 + 0.0002 3.8094 + 0.0002 3.6275 + 0.0002 3.6136 + 0.0002 3.6139 + 0.0002 3.6120 + 0.0002

D. Sample Calculations Q-test

where Q is the ratio compared to Qtab, xq is the suspected value, xn is the value closest to the suspected and w is the range of the entire set. H: Qexp = |3.8094 – 3.6275| = 0.66850 (0.27210) L: Qexp = |3.5373 – 3.5928| = 0.20397 (0.27210) Mean (X)

X = 3.5928 + 3.6083 + 3.6210 + 3.5373 + 3.6234 + 3.8094 = 3.6320 6 x= = 0.0005 Standard Deviation (S)

S= = 0.092447

Relative Standard Deviation (RSD) * 1000 ppt = 25.453 ppt

Range (R)

R = Xhighest - Xsmallest= (3.8094 – 3.5373) = 0.27210

Relative Range (RR) RR = = * 1000 ppt = 74.917 ppt

Confidence Limit (CL)

= 3.63 + 0.14

E. Discussion Standard deviation is a statistical measure of dispersion of values. It represents how closely a set of numbers is around its mean or expected value. It is an important concept since it is a precise indicator of the degree of variability within a set of numbers. Smaller standard deviation...

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