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Frequency Distribution of Rejected Circuit Boards X Week
On the basis of the information provided in Table 1 above the first conclusion to be drawn is in reference to the data's kurtosis or skewness (peaked ness or flatness); i.e., leptokurtic, platykurtic, or mesokurtic. Visual interpretation suggests that there are no areas of flatness or extreme peakedness. Therefore, the distribution of data falls somewhere in between (mesokurtic/normal). As such the assumption can be made that the data is normal but with bi-modal characteristics (i.e., two closely similar high rejection scores; 26 and 24). Extreme caution must be exercised in acceptance of this conclusion, as there is no information as to the ratio of rejected circuit boards to accepted circuit boards.
In support of the data being normally distributed the standard deviation (() of the scores was calculated. The "(" symbol is used as the assumption is being made that the data presented represents the entire number of rejected circuit boards produced rather than a sampling of a greater population. When in doubt the data is assumed to represent a population rather than a sample of a population.
In any statistical analysis the standard deviation mathematical quotient is representative of the degree to which a difference exists between a score distance and the mathematical mean of the group. As the Excel Program only permits cells up to a 30 count the more conventional hand calculation method was used. For the current set of data the calculated standard deviation is expressed by the following formula:
((((2-((()2
N = 38
(X = 684
((X)2 = 467,856
((2 = 12,528
Standard Deviation = ±2.416
A standard deviation of ±2.416 for the ungrouped date suggests that the rejection of the circuit boards within each week fluctuates above and below its mean of rejection by approximately ±2.416 points.
With a mean rejection rate of 18 pieces per week rejection the probability of a 15 piece rejection rate is highly probable with a standard deviation of ±2.416 (15 + 2.415 = 17.415). Caution must be exercised at this point, as "predictive" statistical measures must be employed in order to determine the exactness of the prediction. More specifically the probable rate would be 18:1 (r/N).
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