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Overall Quality Manufacturing, Statistics Problem Example

Pages: 3

Words: 725

Statistics problem
Overall Quality Manufacturing Frequency Percent Frequency
2 9 24.3%
3 20 54.1%
4 7 18.9%
5 1 2.7%

Overall Quality Manufacturing

The sample size in this case is thirty seven observations. The main measures of central tendency, mean, median, and mode, are all three in this sample. It has a variance of .55 and a standard deviation of .74. This puts 54% of observations within one standard deviation, 43% within two, and 2.7% within three. However, the discreet nature of the possible answers, four possible answers, makes this analysis slightly less valuable than normal.

Overall Quality Design Frequency Percent Frequency
2 11 29.7%
3 19 51.4%
4 6 16.2%
5 1 2.7%

Again, the sample size here is thirty-seven. The mode and median is again three, but this time the mean is slightly lower at 2.92. The variance is .58 with a standard deviation of .76. 51% of the observation is within one standard deviation, 46% within two, and 2.7% within three.  Again the nature of the possible answers does not lend itself well to this sort of analysis.

Overall Quality Design

Origin 2 3 4 5 Total
United States 2 8 3 0 13
Pacific Rim 4 8 1 1 14
Europe 3 5 2 0 10
Total 9 21 7 1 37

The most significant relationship seems to be between United States manufacturing and quality. Each of the three regions produces a similar proportion of 3 ratings, but the United States has significantly more 4 ratings at the expense of 2 ratings. The Pacific Rim and Europe have similar ratings, except Japan has the only 5 rating given while Europe simply has two four ratings instead of Japan’s one.

Origin 2 3 4 5 Percent of Whole
Percent of United States 15.4 61.5 23.1 0.0 35.1
Percent of Pacific Rim 28.6 57.1 14.3 7.1 37.8
Percent of Europe 30.0 50.0 20.0 0.0 27.1
Percent of Whole 24.3 56.8 18.9 2.7 100

Again, this shows that the United States has a lower percentage of two ratings and a larger percentage of four ratings than either other region. The Pacific Rim has the only five rating in all the data, but the lowest rate of fours. If you look at four and five ratings together, grouping them in a greater than three category, the Pacific Rim countries have a similar rate to Europe.  Also, this rate is slightly below that of the United States greater than three rates. The United States also has a larger rate of three ratings with a lower rate of two ratings than the others.

Origin 2 3 4 5 Total
United States 2 10 1 0 13
Pacific Rim 4 6 4 0 14
Europe 5 3 1 1 10
Total 11 18 8 1 37

Note: The directions for Step 8 said to describe the relationship between origin and manufacturing rating. Since this was done in Step 4 and since this table represents design rating, I have assumed that it was intended to ask about design rating.

Here it looks like Europe is worse at designing than the other two regions. Half of its ratings are two and even with the single five rating, it still has a lower mean. The United States design produces a great deal of threes, while Japan has the most fours in absolute and rate terms.

Origin 2 3 4 5 Percent of Whole
Percent from United States 15.4 76.9 7.7 0 35.1
Percent from Pacific Rim 28.6 42.9 28.6 0 37.8
Percent from Europe 50 30 10 10 27.1
Percent of Whole 29.7 48.6 21.6 2.7 100

The three countries are very different in terms of design ratings compared to manufacturing ratings, which were largely similar. The first thing that jumps out is the huge proportion of three ratings among American companies. The Pacific Rim features the highest right of fours. Finally, Europe mostly has the most two ratings. Interestingly, if you divide it into three categories, two, three, greater than three, each region has the highest rate in one category, the lowest in another, and consequentially the middle rate in the third.

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