Question

The mean score on the quiz was 6.625 with a population standard deviation of 1.9. Which of the following statements best describes the quiz scores? (DOK 3) All of the earned scores are within one standard deviation of the mean. All of the earned scores are within two standard deviations of the mean. All of the earned scores, except for one, is within two standard deviations of the mean. The value of 10 is an outlier so it should be removed from the data set.

Answer 1

The range of the scores is given by :

For one standard deviation :

`\text{range}=6.625\pm1.9*1`

The range is :

6.625 - 1.9 = 4.725

6.625 + 1.9 = 8.525

So it follows that the range of the scores is from 4.725 to 8.525

And it concludes that NOT all scores are within the one standard deviation because the histogram shows a score of 2, 9 and 10.

So choice A is NOT VALID

For two standard deviations :

`\text{range}=6.625\pm1.9*2`

The range is :

6.625 - 1.9(2) = 2.825

6.625 + 1.9(2) = 10.425

So it follows that the range of the scores is from 2.825 to 10.425

And it concludes that All of the scores are within the two standard deviation except for the score "2".

So Choice B is also NOT VALID

But the Choice C, will satisfy this condition. For all of the earned scores, except for one, is within two standard deviations of the mean.

So the answer is Choice C or Third Option.