Question

Define a healthy brand of cereal to be one with both low sodium and low sugar. Given a data set of different cereal brands with their respective amounts of sodium and sugar, what graphical (charts, plots, etc) and numerical (mean, mode, variance, etc) data summary methods might be useful in determining what brand of cereal is the healthiest?

Answer 1

Given:
Data set: different cereal brands with their respective amounts of sodium and sugar

For example: Brand 1 : amount of sodium = X₁%

                                    amount of sugar = Y₁ %

                      Brand 2 : amount of sodium = X₂%

                                    amount of sugar = Y₂ %

etc.

To determine what brand of cereal is the healthiest:

i.e.,

which brand has lowest :Sodium: minimum of X₁, X_{2 ,}    & lowest Sugar minimum of Y₁, Y_2.,,,,among Brand 1, Brand 2 etc.

(i) Appropriate graphical method: Pie charts.

Reason: We can choose which brand has minimum of X₁, X_{2 ,}      and also has got minimum of Y₁, Y_2.,,,,from the minimum sector areas of the pie charts

(ii) Appropriate numerical data summary: Mode

Reason: Mode gives the maximum value of the data. So, find out the mode of the negatives of X values. It will give the minimum of X. Find out the mode of the negatives of Y values. It will give the minimum of Y. The corresponding Brand will be the healthiest brand with minimum sodium and minimum sugar.