The accompanying data set contains country-level health and population measures for 38 countries from the World Bank’s 2000 Health Nutrition and Population Statistics database. For each country, the measures include death rate per 1,000 people (Death Rate, in %), health expenditure per capita (Health Expend, in US$), life expectancy at birth (Life Exp, in years), male adult mortality rate per 1,000 male adults (Male Mortality), female adult mortality rate per 1,000 female adults (Female Mortality), annual population growth (Population Growth, in %), female population (Female Pop, in %), male population (Male Pop, in %), total population (Total Pop), size of labor force (Labor Force), births per woman (Fertility Rate), birth rate per 1,000 people (Birth Rate), and gross national income per capita (GNI, in US$). The accompanying table shows a portion of the data.

a. Perform k-means clustering to group the 38 countries into four clusters according to their health measures (i.e., Death Rate, Health Expend, Life Exp, Male Mortality, and Female Mortality) only. Is data standardization necessary in this case? 

b. What are the size and the average GNI per capita for the largest cluster of countries?

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Country Name Argentina Austria 1 Switzerland Death Health Rate Expend 7.8 706.9 9.6 2415.78 E 8.7 3540.86 ⠀ GNI 7440 26790 E 43460