Analyze (using statistics you have learned about central tendency and variation)

Question

Analyze (using statistics you have learned about central tendency and variation) whether you believe the percentages of colors from the manufacturer are correct based on your sample of 10 bags of M&M's.

State your conclusions in business terms of what the study shows.

M N Q R T U V W XYZ AA AB AD Bags 66% +1 |-1 7.56 4.44 95% 9 | 10 Total % of Total | Expected 10.85% | 30.00% 13.20% | 20.00% 9.40% | 20.00% 22.60% | 10.00% 22.60% | 10.00% 21.34% | 10.00% 100.00% | 100.00% + 2 1-2 + 3 |-3 9.13 2.87 10.69 1.31 16.47-1.87 12.61-2.21 16.32-5.92 Mean l StdDev ) 3 Color 4 Brown 6.00 7.30 5.20 12.50 12.50 11.80 55.30 1.56 3.0610.36 4.2413.41 1.19 3.71 2.3714.87 10.13 17.24 7.7619.61 5.39 4.0316.538.4720.57 4.43 24.60 0.40 4.0515.857.75 19.90 3.7023.95-0.35 1.42 Yellow 12 73 6 Red 7 Orange..16.111612.11...12 9 Blue 0 Total 8.91 1.49 12 125 6 125 118 553 16 18 14 12 10 53 Green 16 16 13 57 57 57 56.72 53.8858.14 52.46 59.55 51.05 12 Total The Color Mixture in Your Bag of M&Ms; Is a Science 15 140 120 M&M;'s Milk chocolate: 30% brown, 20% yellow, 20% red, 10% orange, 10% green, and 10% blue. M&M;'S Peanut: 20% brown, 20% yellow, 20% blue, and 20% red, 10% orange, and 10% green. M&M;'S Peanut Butter and Almond: 20% brown, 20% yellow, 20% green, 20% blue, and 20% red. 20 100 Brown Yellow Red 4 - Orange Green 7 40 Blue 28 32 Yellow Red Blue

Explanation / Answer

Observations

1. In terms of observed % and expected %, wide deviations are seen – Brown 11 vs 30; Red 9 vs 20; Ornage and Green 23 vs 10 and Blue 21 vs 10

2. Similarly, wide variation exists in both measures – mean ranging from 6 to 12.5 (more than double) and standard deviation ranging from 1.06 to 4.05 (a four-fold deviation)

3. These deviations give rise to the suspicion that the figures given by the manufacturer are not correct.

4. Bar diagrams also bring out the same features.

5. However, there are no outliers even at 95% confidence.

DONE

[Additional inputs: At this early stage of statistical knowledge, it is difficult to make firm statements. At a later stage when Statistical Inference is covered, more emphatic statements can be made]

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