What makes a person educated?
Education remains a concept as difficult to define and as open to debate as it is essential to our identity. Is a skilled artisan with no formal schooling educated? Is a wise grandmother with eighty years of life experience, but only a third-grade education educated? Is Bill Gates, who dropped out of Harvard as a junior to found Microsoft, more or less educated than his classmates who stayed in school? When we are seeking education, are we looking for knowledge, wisdom, skills, or all three?
This is a wonderful question. I would distinguish between formal education and informal education. I would also distinguish between education and wisdom. These two distinctions cover the situations that you mention here.
The grandmother is not educated. She does not have any (from what you say) of the knowledge that comes with education. She would not, for example, be able to do algebra or explain the idea of supply and demand. However, she is probably wise. That is, she knows what is approprite to do in various life situations that she has ecountered. This is very important, but it is not education.
Bill Gates has more education than his ex-classmates in certain areas. True, he did not learn these things in school, but he did learn them informally. Education is the acquisition of knowledge and he has acquired knowledge on a relatively broad range of subjects (computers, business, management, things having to do with his foundation). It is informal education because he did not gain it in school, but it is still education.
Education, then, is the acquisition of knowledge. It can be formal or informal, but it is not the same thing as the wisdom that comes with experience and age.
Education can also have negative effects too, such as being taught or 'educated' to hate others for some reason or other, even to the extent where terrorism, murder and other crimes against society are considered legitimate.