Yisenia spun a spinner 29 times, and the results are shown in the following table.

Number
Frequency

1


10


2


9


3


10



Nicole models Yisenia's experiment by drawing a spinner. On Nicole's spinner, the numbers 1 and 2 split one-half of the spinner, and the number 3 takes up the other half of the spinner.
Is Nicole's model a good model for Yisenia's experiment? Why or why not?

Responses
No, the spinner should be split into three approximately equal sections.

Yes, there are three numbers and three sections.
.
Yes, the number 3 has the highest frequency.

No, the number 2 should take up approximately half of the spinner.

1 answer

To determine if Nicole's model is a good representation of Yisenia's experiment, we need to consider the relative frequencies of the outcomes based on the spinner results.

Yisenia spun the spinner 29 times with the following frequencies:

  • Number 1: 10 times
  • Number 2: 9 times
  • Number 3: 10 times

From this, we can calculate the relative frequencies:

  • Number 1: \( \frac{10}{29} \)
  • Number 2: \( \frac{9}{29} \)
  • Number 3: \( \frac{10}{29} \)

Now, looking at Nicole's spinner, she has divided it as follows:

  • Numbers 1 and 2 together occupy one-half (50%).
  • Number 3 occupies the other half (50%).

Now let's analyze:

  • In Yisenia's experiment, quasi-equal outcomes for numbers 1 and 3 suggest that both 1 and 3 are more likely than 2, but all values should proportionally reflect their established frequencies via the model.
  • If number 1 takes approximately 34.48% (10/29) of the spinner, number 2 takes approximately 31.03% (9/29), and number 3 takes approximately 34.48% (10/29). This diversifies compared to Nicole’s model which does not adequately depict the higher probability for numbers 1 and 3 versus number 2.

Given this analysis, the most appropriate response is:

No, the spinner should be split into three approximately equal sections.

This is because the spinner must reflect the distribution of outcomes according to their frequencies rather than just being divided into halves, which does not represent the actual outcomes from Yisenia's experiment.