Before you can do one of these histograms by hand, you first have to start with a frequency table, so if you haven't already watched that video, do so now!. Then the histogram is easy, just be sure to use class boundaries properly.
There are lots of ways to define what an outlier is, other than a "way out there" piece of data you want to just ignore to make your homework easier. This video explains what outliers are, and the most common way of defining them.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)