The answers to this problem are based on R version 3.5.3. To replicate the results with newer versions of R, execute the following line of code at the beginning of the R session or your R code: suppressWarnings(RNGversion("3.5.3")). Perform k-means clustering on the accompanying data set.

a. Use all variables in the analysis. Do not standardize the variables. Set the number of clusters to 3. What are the size and average distance for the largest cluster? (Round "Average value" to 2 decimal places.)

Size of the largest cluster?

Average distance for the largest cluster?

b. Specify the same settings as in part a, but standardize the variables. What are the size and average distance for the largest cluster? (Round "Average value" to 2 decimal places.) Size of the largest cluster?

Average distance for the largest cluster?

x1	x2	x3
14.8	9045.26	0.2498
16.4	7529.96	0.2934
15.5	9566.1	0.1765
12.2	8434	0.2043
14	5855.51	0.277
16	9402.83	0.2336
12.5	6629.25	0.1205
16	9211.96	0.226
15.6	8783.87	0.2889
15.3	10163.11	0.264
15.6	8054.17	0.3141
15	10140.4	0.1692
16.8	4144.14	0.101
16	6334.28	0.2455
14	7437.5	0.163
11.7	8182.15	0.2886
12.6	4654.79	0.1284
14.8	8719.27	0.1453
16.2	7389.69	0.2554
13	6935.56	0.1201
13.4	7400.76	0.2368
14.4	9371.64	0.2079
15.5	12243.79	0.1143
14.2	7379.12	0.1041
14	6771.33	0.2913
15	5027.22	0.1036
15.1	11273.03	0.1666
14.4	7519.27	0.2004
13.9	7440.93	0.2236
14.3	7146.74	0.3534
14.4	8569.04	0.1383
12.5	6756.18	0.2243
14.7	7607.36	0.2444
15.2	6929.7	0.2503
12.2	8933.44	0.2111
14.3	6705.31	0.3389
16.5	9928.14	0.2631
16.3	9383.32	0.2292
14.5	8261.26	0.226
13.9	4968.51	0.2353
14.5	8086.05	0.2659
15.6	12626.77	0.1927
14.9	6424.36	0.2788
13.9	9499.87	0.2162
14.4	8748.67	0.249