How do I explain Part B?

Question

Jose and Mirka each asked 50 students in their school whether they prefer comedy or action movies. The table

gives the results of their poll.

                           comedy           action

Jose's group             20                 30

Mirka's group           25                  25

 

PART B

When all the students at their school were surveyed, 70% preferred comedy. Explain a possible reason why Jose’s

and Mirka’s sample groups were not a good representation of the students in their school

Answer 1

Mirka's sample group was not a good representation of the students at their school because Mirka's sample resulted in 25 favoring comedy and 25 favoring action -- which would be half and half, or 50-50.  That would not match up with 70% preferring comedy because only 50% of Mirka's group preferred comedy.

 

Furthermore, Jose's group held that 20/50 or 2/5 preferred comedy.  2/5 = .40 or 40%, so that would not be near 70% which was the result of the school survey.  

 

Some reasons why Mirka and Joel's sample groups were not a good representation of the entire student body may be that:

 

(1) Mirka and Joel interviewed only one gender, such as only girls, or only boys;

(2) Mirka and Joel interviewed only one grade level, such as only 5th graders;

(3)  Mirka and Joel did not take care to include an equal number of girls and boys;

(4)  Mirka and Joel could have asked their interview questions differently, not all in the same way, which may have influenced the responses they received.

Answer 2

The weakness of samples is that it is only an approximation. Different ages, genders, upbringing may change what the final tally is. We also do not know just how many people are in the school, so we do not know how large the sample size is in relation to the total number of students.