Helena asked five drama club members in her homeroom how many tickets they had sold. The mean number of tickets sold was 16. Then she took ten random samples from the entire drama club of 75 students. The mean number of tickets sold was 22.5.

Compare the means. Is one sample a better representation? Explain why or why not.

Sample Response: The sample from the drama club is a more accurate sample. It is a random sample that represents the target population and it is large enough for inferences.

Number of members chosen by Helena in her homeroom = 5

Mean number of tickets = 16

So, total candidates who had purchased ticket = 16 × 5= 80

Now, number of candidates chosen randomly = 10

So, total candidates who had purchased ticket = 22.5 × 10=225

No, one sample can't be a better representation by choosing randomly a group of members.

In Sample 1 , we are considering only 5 drama numbers.

And In Sample 2, we are considering 10 random samples among 75 members.

The mean in two cases varies by (22.5-16=6.5) which is large because we are considering number of tickets sold by members of club.

It would have been better if she has taken more than 3 random samples of 15  students ,among 75 students, then she would have got appropriate mean or value near the mean.

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