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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 should compare the frequencies obtained from the experiment to the areas of the sections on Nicole's spinner.

Yisenia's results show the following frequencies:

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

This totals to 29 spins.

To find the proportion of each number based on the results:

  • Proportion of 1: 10/29
  • Proportion of 2: 9/29
  • Proportion of 3: 10/29

Now, let's analyze Nicole's spinner:

  • Numbers 1 and 2 together cover half the spinner (50%)
  • Number 3 covers the other half (50%)

This distribution does not accurately reflect the experimental results, because:

  • Numbers 1 and 3 have higher frequencies but are not adequately represented on Nicole's spinner.
  • Number 2 is given half the spinner, which is disproportionate compared to its frequency.

Based on this analysis, the correct response would be:

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