This question is from the book "Teach Yourself Statistics" by Richard Goodman: https://archive.org/details/TeachYourselfStatistics
The solution provided is: $26.89$ and $45.14$. How do I get this solution?
I took the mid-values of the intervals and my solution was $26.39$ and $44.6$. Am I missing something?
This kind of problem brings two mistakes.
The first mistake is the middle of the class. If someone is aged between $15$ and $19$ (rounded to nearest integer), his real age is between $15$ (included) and $20$ (excluded). E.g. someone aged $19$ years and $364$ days will still be considered $19$ years old. The middle of the class is then $17.5$. All the classes' middle is Up by $0.5$, then the mean is also up by $0.5$. Your first mean become $23.89$.
The second mistake is with the open class at the end. Since we don't know the upper limit, we suppose the class is as wide as the other. We suppose people are aged between $55$ (included) and $60$ (excluded). The middle of this class is $57.5$. With these classes' middle, we have a mean of $45.095$.
Hope it helps