Additional Maths Sba EXAMPLE

Title: Is the net Weight of Grace Chicken Soup Actually 60 grams?
Name of Candidate: Sba Example
Center Number: 100033
Candidate Number:
Teacher: Anybody

Acknowledgement

I must first thank the Lord God for blessing me with the knowledge, wisdom, strength and understanding in completing my Internal Assessment. Secondly, I would like to express my sincerest gratitude to my teacher Mr. Darron Fraser who has remain committed for several years, gone beyond his call of duty in his efforts to adequately prepare me for this Mathematics examination.
By no means least, I would like to thank National Processors, a division of GK Foods and Services, Grace Kennedy, for their kindness in donating the time and the required samples that were fundamental in completing this assignment. Again I say to you all, thanks a million!

INTRODUCTION
A group visited the National Processors, met with the Operations Manger. Protective garments were issued before entering Production floor and also guidelines for visitor’s entry to restricted area.
At National Processors, statistics play a very critical role in successfully carrying out their day-to-day affairs as a Dry Pack Plant. Four different Dry products are chicken, cock (local and UK) and fresh start.
WEIGHT SPECIFICATIONS

LOWER CRITICAL LIMIT
ACTION LEVEL

TARGET
ACTION LEVEL
UPPER CRITICAL LIMIT
CHICKEN -net wt
59.5
60
62
64
65
NOODLES
42.6
43.0
44.4
45.8
46.4
SPICE
16.9
17.0
17.6
18.2
18.6
Prior to starting production at the beginning of each day, the weights of each product have to first be checked and recorded by a Quality Control representative and during production; the process is thereafter repeated every 30 minutes for consistency. One such product is the popular Grace Chicken Soup and the weights of 30 random samples were taken and recorded. This sampling method used in the factory is Stratified Sampling. However, sampling method used by company for market research is Quota Sampling.

RESEARCH QUESTIONS

1.) Is the net weight of the product actually 60 grams?
2.) Does the weights of the product (Chicken Soup) meet the manufacturing parameters of the company?

How the data was obtained
A visit was made to the company.
An electronic balance was used to obtain the net weight of every 10th sample and the results were recorded in a suitable data table.

Raw Mass of Chicken Soup Packages:grams
60.8 61.0 64.0 63.3 61.0 62.0 62.3 61.2 61.9 61.1 63.0
60.5 63.9 62.4 61.6 62.9 61.9 61.4 61.2 62.8 61.9 61.8
62.6 61.9 61.3 61.5 61.7 61.5
STEM AND LEAF DIAGRAM

60
61
62
63
64
5 8
0 0 1 2 2 3 4 4 5 5 6 6 7 7 8 9 9 9
0 3 4 6 8 9
0 3 9
0
KEY 60/5=60.
Table Showing the Weights of 30 chicken Soups
MASS(grams)
Mid-point
FREQUENCY
60 <61
60.5
2
61<62
61.5
18
62<63
62.5
6
63<64
63.5
3
64<65
64.5
1

ANALYSIS
CALCULATION FOR MEAN

Total 22.42

Key 60/5 means 60.5
Mean = ∑ = = 62
SD = 2

=
SD = = 0.88

CALCULATION FOR THE MEDIAN AND QUARTILES

Median n =30 n+1=31/2=15.6 15th and 16th value n+1 =32/2=16
(Q2) median =61.7 + 61.7
=123.4 /2 =61.7

Lower Quartile
¼(n+1)
¼ (30 + 1) =7.75
7th and 8th value
(Q1) LQ=61.2+61.3
=122.5/2=61.25

Upper Quartile ¾ (n+1) ¾ (31) = 23.25

23rd and 24th value

(Q3)= 62.4 + 62.6

= 125 /2 =62.5

Graph of Mass

BOX AND WHISKER DIAGRAM

DISCUSSION AND CONCLUSION

The Mean was found to be 62, while the Standard Deviation was found to be 0.88. The Median was calculated at 61.7, the Lower Quartile 61.25 and the Upper Quartile, 62.5. The Box and Whisker graph was positively skewed to the right with majority of the weights falling between 61.25 and 63.0. The modal value according the Stem and Leaf plot was found to be 61.9.

Conclusion
It can be concluded from the data that the central value was below the required net weight that was on the original package. Only the mean was 62 while the other measures were below the weight stated on the package.
Therefore further testing is required on a larger sample to determine if the net weight is actually 62 grams or less.

Bibliography

Brase, C. (2007). Understandable statistics 9th Edition. Boston: Houghton Mifflin Harcourt

Brewer ,C. (1995). Music Memory Activities. Retrieved from http://www.songsforteaching.com/brewer/memory.htm on February 24,2011

Bulmer, M. (1979). Principles of statistics. New York: Dover Publications

Davisson, L., and Gray(2005). An Introduction to Statistical Signal Processing. Cambridge University Press

Mc Cabe G., and Moore (2003). Introduction to the Practice of Statictics 2nd Edition. New York: W. H. Freeman & Company

Freedman, D., Pisani and Purves. (2007). Statistics 4th Edition. New York: W.W. Norton & Company

Bibliography: Brase, C. (2007). Understandable statistics 9th Edition. Boston: Houghton Mifflin Harcourt Brewer ,C. (1995). Music Memory Activities. Retrieved from http://www.songsforteaching.com/brewer/memory.htm on February 24,2011 Bulmer, M. (1979). Principles of statistics. New York: Dover Publications Davisson, L., and Gray(2005). An Introduction to Statistical Signal Processing. Cambridge University Press Mc Cabe G., and Moore (2003). Introduction to the Practice of Statictics 2nd Edition. New York: W. H. Freeman & Company Freedman, D., Pisani and Purves. (2007). Statistics 4th Edition. New York: W.W. Norton & Company