Respuesta :

Answer:  Choice C.  mean > median

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Explanation:

Multiply each measure with their corresponding frequency.

  • 8*1 = 8
  • 10*3 = 30
  • 14*2 = 28

Add up those products: 8+30+28 = 66

Then divide by the total frequency n = 1+3+2 = 6 to get 66/6 = 11 as the mean.

mean = 11

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Since we have n = 6 values in this list, this means the median is between slot n/2 = 6/2 = 3 and slot 4.

Note how that places us in the middle row because 1+3 = 4 encapsulates both of those slots mentioned. So the median is 10.

Or you could list out the values in roster notation {8, 10, 10, 10, 14, 14} to see that {10,10} occupy the middle most slots. So the median is (10+10)/2 = 20/2 = 10.

median = 10

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The mode is simply the most frequent value. The table shows that mode = 10 since it occurs 3 times, compared to 8 showing up 1 time and 14 showing up twice.

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We have the following summary

  • mean = 11
  • median = 10
  • mode = 10

With that in mind, let's go through the answer choices.

  1. We can see that mean < mode is false, since it should be mean > median, so cross choice A off the list.
  2. mean = median is also false, so choice B is crossed off as well.
  3. mean > median is true since 11 > 10 is true. Choice C is the answer. Note how this being true directly contradicts choice B, which is another reason to see why choice B is false.
  4. median > mode is false because 10 > 10 is false. It should be median = mode. Choice D is crossed off the list.

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