Question

If someone said that the mean age of everyone in your algebra class is about \(16 \frac{1}{2}\) years, do you think the age of the teacher was included in the calculation? Explain.

Short answer

The age of the teacher was likely not included in the calculation of the mean age. Including the teacher's age would likely have resulted in a significantly higher mean age for the class.

Step-by-step solution

Understand the problem

To answer this question, one needs to understand how average or mean is calculated. The mean is calculated by summing up all the individual units of a set and then dividing by the total count. Here, if the teacher's age was included in the calculation, the calculated mean would be significantly higher than 16.5, assuming that the teacher is older than the students.

Analyze the stated mean age

The stated mean age for the algebra class is 16.5 years. Generally, students in a high school algebra class could be around this age, but a teacher would be considerably older.

Draw a conclusion

Given that the average or mean age is pretty close to the expected age of the students, it's likely that the teacher's age was not included in the calculation. Should the teacher's age be included, the mean age would likely be raised significantly above the student age range, assuming the teacher is older