Case Study-1

Case Study- Mr. Bean visited a departmental store in Triplicane at Chennai on 1st March and chooses different types of food items that include nutrition information on its packaging. For each food Mr. Bean observed and identified the amount of fat (gms) and the sodium content ( mgs/100gms) per serving and recorded in the following table. Sl. No. Product Items Fat (gm/100gms) Sodium (mg / 100gms) . Dates . . . Appalam . . Energy drink . . Gulabjamun Powder . . Atta . . . Athi fruits . . Alu Muttar mix - - Correlation and Regression analysis . P opcorn . . . Perungayum . . Mushroom . . Friut juice . . Choclate . . . Rava . Biscuit . . Snacks . Mr. Bean wants to establish some statistical relationship between the above mentioned food contents. Here the variable under study are X and Y which represents the amount of Fat content and the amount of Sodium content in each food items respectively. Thus Mr. Bean gets a pair of values ( X , Y ) for each food item. Mr. Bean further found the average fat content in all the food items is X = . (gms/100g) and the average sodium content in all the items is Y = . (mg/100g). Further, it was identified that the minimum amount of fat contained in Tropicana fruit juice is . (g/100gms) and the maximum amount of fat contained in Lays is . (g/100gms). Thus the fat contained in all the food items is ranging from . (g/100gms) to . (g/100gms). Similarly, the minimum amount of sodium content contained in Kelloggys Choco is . (mg/100gm) and the maximum amount of sodium content in Bhindhu appalam is (mg/100gm). So, the measure of range of fat content and sodium content in all the items are .4gm and . (mg/100gm) respectively. Besides, Mr. Bean is interested in knowing the variation of each individual item from the mean of all observations. He attempted another measure of dispersion known as standard deviation. The measure of standard deviation indicates that there is an average deviation of . (g/100gms) in fat content and . (mg/100gms) in sodium content of all the food items. Further, Mr. Bean is keen on finding the association between the variables X and Y . So, the correlation analysis has been carried out. The correlation coefficient r ( X , Y )= . indicates that there is . % positive association between sodium content and the amount of fat content. Thus from this study Mr. Bean inferred and convinced that the nutrition information on the packaging of each food item is sufficient.