Customer Rating of Breakfast Cereals.The datasetCereals.csvincludes nutritional information, store display, and consumer ratings for 77 breakfast cereals.

Data Preprocessing.Remove all cereals with missing values. Using R:

1. Apply hierarchical clustering to the data using Euclidean distance to the normal- ized measurements. Compare the dendrograms from single linkage and complete linkage, and look at cluster centroids. Comment on the structure of the clusters and on their stability.Hint: To obtain cluster centroids for hierarchical clustering, compute the average values of each cluster members, using theaggregate()function.
2. Which method leads to the most insightful or meaningful clusters?
3. Choose one of the methods. How many clusters would you use? What distance is used for this cutoff? (Look at the dendrogram.)
4. The elementary public schools would like to choose a set of cereals to include in their daily cafeterias. Every day a different cereal is offered, but all cereals should support a healthy diet. For this goal, you are requested to find a cluster of "healthy cereals." Should the data be normalized? If not, how should they be used in the cluster analysis?

Copy of Cereals.csv:

name,mfr,type,calories,protein,fat,sodium,fiber,carbo,sugars,potass,vitamins,shelf,weight,cups,rating

100%_Bran,N,C,70,4,1,130,10,5,6,280,25,3,1,0.33,68.402973

100%_Natural_Bran,Q,C,120,3,5,15,2,8,8,135,0,3,1,1,33.983679

All-Bran,K,C,70,4,1,260,9,7,5,320,25,3,1,0.33,59.425505

All-Bran_with_Extra_Fiber,K,C,50,4,0,140,14,8,0,330,25,3,1,0.5,93.704912

Almond_Delight,R,C,110,2,2,200,1,14,8,,25,3,1,0.75,34.384843

Apple_Cinnamon_Cheerios,G,C,110,2,2,180,1.5,10.5,10,70,25,1,1,0.75,29.509541

Apple_Jacks,K,C,110,2,0,125,1,11,14,30,25,2,1,1,33.174094

Basic_4,G,C,130,3,2,210,2,18,8,100,25,3,1.33,0.75,37.038562

Bran_Chex,R,C,90,2,1,200,4,15,6,125,25,1,1,0.67,49.120253

Bran_Flakes,P,C,90,3,0,210,5,13,5,190,25,3,1,0.67,53.313813

Cap'n'Crunch,Q,C,120,1,2,220,0,12,12,35,25,2,1,0.75,18.042851

Cheerios,G,C,110,6,2,290,2,17,1,105,25,1,1,1.25,50.764999

Cinnamon_Toast_Crunch,G,C,120,1,3,210,0,13,9,45,25,2,1,0.75,19.823573

Clusters,G,C,110,3,2,140,2,13,7,105,25,3,1,0.5,40.400208

Cocoa_Puffs,G,C,110,1,1,180,0,12,13,55,25,2,1,1,22.736446

Corn_Chex,R,C,110,2,0,280,0,22,3,25,25,1,1,1,41.445019

Corn_Flakes,K,C,100,2,0,290,1,21,2,35,25,1,1,1,45.863324

Corn_Pops,K,C,110,1,0,90,1,13,12,20,25,2,1,1,35.782791

Count_Chocula,G,C,110,1,1,180,0,12,13,65,25,2,1,1,22.396513

Cracklin'_Oat_Bran,K,C,110,3,3,140,4,10,7,160,25,3,1,0.5,40.448772

Cream_of_Wheat_(Quick),N,H,100,3,0,80,1,21,0,,0,2,1,1,64.533816

Crispix,K,C,110,2,0,220,1,21,3,30,25,3,1,1,46.895644

Crispy_Wheat_&_Raisins,G,C,100,2,1,140,2,11,10,120,25,3,1,0.75,36.176196

Double_Chex,R,C,100,2,0,190,1,18,5,80,25,3,1,0.75,44.330856

Froot_Loops,K,C,110,2,1,125,1,11,13,30,25,2,1,1,32.207582

Frosted_Flakes,K,C,110,1,0,200,1,14,11,25,25,1,1,0.75,31.435973

Frosted_Mini-Wheats,K,C,100,3,0,0,3,14,7,100,25,2,1,0.8,58.345141

"Fruit_&_Fibre_Dates,_Walnuts,_and_Oats",P,C,120,3,2,160,5,12,10,200,25,3,1.25,0.67,40.917047

Fruitful_Bran,K,C,120,3,0,240,5,14,12,190,25,3,1.33,0.67,41.015492

Fruity_Pebbles,P,C,110,1,1,135,0,13,12,25,25,2,1,0.75,28.025765

Golden_Crisp,P,C,100,2,0,45,0,11,15,40,25,1,1,0.88,35.252444

Golden_Grahams,G,C,110,1,1,280,0,15,9,45,25,2,1,0.75,23.804043

Grape_Nuts_Flakes,P,C,100,3,1,140,3,15,5,85,25,3,1,0.88,52.076897

Grape-Nuts,P,C,110,3,0,170,3,17,3,90,25,3,1,0.25,53.371007

Great_Grains_Pecan,P,C,120,3,3,75,3,13,4,100,25,3,1,0.33,45.811716

Honey_Graham_Ohs,Q,C,120,1,2,220,1,12,11,45,25,2,1,1,21.871292

Honey_Nut_Cheerios,G,C,110,3,1,250,1.5,11.5,10,90,25,1,1,0.75,31.072217

Honey-comb,P,C,110,1,0,180,0,14,11,35,25,1,1,1.33,28.742414

Just_Right_Crunchy__Nuggets,K,C,110,2,1,170,1,17,6,60,100,3,1,1,36.523683

Just_Right_Fruit_&_Nut,K,C,140,3,1,170,2,20,9,95,100,3,1.3,0.75,36.471512

Kix,G,C,110,2,1,260,0,21,3,40,25,2,1,1.5,39.241114

Life,Q,C,100,4,2,150,2,12,6,95,25,2,1,0.67,45.328074

Lucky_Charms,G,C,110,2,1,180,0,12,12,55,25,2,1,1,26.734515

Maypo,A,H,100,4,1,0,0,16,3,95,25,2,1,1,54.850917

"Muesli_Raisins,_Dates,_&_Almonds",R,C,150,4,3,95,3,16,11,170,25,3,1,1,37.136863

"Muesli_Raisins,_Peaches,_&_Pecans",R,C,150,4,3,150,3,16,11,170,25,3,1,1,34.139765

Mueslix_Crispy_Blend,K,C,160,3,2,150,3,17,13,160,25,3,1.5,0.67,30.313351

Multi-Grain_Cheerios,G,C,100,2,1,220,2,15,6,90,25,1,1,1,40.105965

Nut&Honey_Crunch,K,C,120,2,1,190,0,15,9,40,25,2,1,0.67,29.924285

Nutri-Grain_Almond-Raisin,K,C,140,3,2,220,3,21,7,130,25,3,1.33,0.67,40.69232

Nutri-grain_Wheat,K,C,90,3,0,170,3,18,2,90,25,3,1,1,59.642837

Oatmeal_Raisin_Crisp,G,C,130,3,2,170,1.5,13.5,10,120,25,3,1.25,0.5,30.450843

Post_Nat._Raisin_Bran,P,C,120,3,1,200,6,11,14,260,25,3,1.33,0.67,37.840594

Product_19,K,C,100,3,0,320,1,20,3,45,100,3,1,1,41.50354

Puffed_Rice,Q,C,50,1,0,0,0,13,0,15,0,3,0.5,1,60.756112

Puffed_Wheat,Q,C,50,2,0,0,1,10,0,50,0,3,0.5,1,63.005645

Quaker_Oat_Squares,Q,C,100,4,1,135,2,14,6,110,25,3,1,0.5,49.511874

Quaker_Oatmeal,Q,H,100,5,2,0,2.7,,,110,0,1,1,0.67,50.828392

Raisin_Bran,K,C,120,3,1,210,5,14,12,240,25,2,1.33,0.75,39.259197

Raisin_Nut_Bran,G,C,100,3,2,140,2.5,10.5,8,140,25,3,1,0.5,39.7034

Raisin_Squares,K,C,90,2,0,0,2,15,6,110,25,3,1,0.5,55.333142

Rice_Chex,R,C,110,1,0,240,0,23,2,30,25,1,1,1.13,41.998933

Rice_Krispies,K,C,110,2,0,290,0,22,3,35,25,1,1,1,40.560159

Shredded_Wheat,N,C,80,2,0,0,3,16,0,95,0,1,0.83,1,68.235885

Shredded_Wheat_'n'Bran,N,C,90,3,0,0,4,19,0,140,0,1,1,0.67,74.472949

Shredded_Wheat_spoon_size,N,C,90,3,0,0,3,20,0,120,0,1,1,0.67,72.801787

Smacks,K,C,110,2,1,70,1,9,15,40,25,2,1,0.75,31.230054

Special_K,K,C,110,6,0,230,1,16,3,55,25,1,1,1,53.131324

Strawberry_Fruit_Wheats,N,C,90,2,0,15,3,15,5,90,25,2,1,1,59.363993

Total_Corn_Flakes,G,C,110,2,1,200,0,21,3,35,100,3,1,1,38.839746

Total_Raisin_Bran,G,C,140,3,1,190,4,15,14,230,100,3,1.5,1,28.592785

Total_Whole_Grain,G,C,100,3,1,200,3,16,3,110,100,3,1,1,46.658844

Triples,G,C,110,2,1,250,0,21,3,60,25,3,1,0.75,39.106174

Trix,G,C,110,1,1,140,0,13,12,25,25,2,1,1,27.753301

Wheat_Chex,R,C,100,3,1,230,3,17,3,115,25,1,1,0.67,49.787445

Wheaties,G,C,100,3,1,200,3,17,3,110,25,1,1,1,51.592193

Wheaties_Honey_Gold,G,C,110,2,1,200,1,16,8,60,25,1,1,0.75,36.187559