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Ryan
Ryan, Engineer
Category: Math Homework
Satisfied Customers: 9060
Experience:  B.S. in Civil Engineering
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I receive 12 surveys ( range 1-5 score) with scores of 4-

Customer Question

I receive 12 surveys ( range 1-5 score) with scores of 4- 5s, 4- 4s, and 4- 3s. For a total of 48 (12 surveys). This give n average of "4" (48/12). Is there an equation I can use to predict how many scores of "5" I need to get an average score of "5"?
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Customer: no
Submitted: 3 months ago.
Category: Math Homework
Expert:  Ryan replied 3 months ago.

Hi,

Thank you for using the site.

Since 5 is the maximum score for a survey, the only way for the average score to be exactly 5 is for ALL of the surveys to have a score of 5. As long as there is a score less than 5 in the set, the average will never be exactly 5, no matter how many surveys are completed.

If you round off the average to a certain number if decimal places, then it would be possible to raise the average to a value that rounds off to 5. The number of additional scores of 5 needed in this case would depend on the desired number of decimal places included in the average.

Thanks,

Ryan

Customer: replied 3 months ago.
ok
Expert:  Ryan replied 3 months ago.

So, for example, if you wanted the average to be 5.00, accurate to 2 decimal places, then you would want the actual calculated average to be a minimum of 4.995.

If we let x be the number of additional scores of 5 that need to be added to the current survey, then you would write the following equation:

(total scores + 5x) / (number of scores + x) = 4.995

So, for the survey totals given in your original posting, the total of the scores was 48, and the number of scores was 12. This would give the following:

(48 + 5x) / (12 + x) = 4.995

You would solve this for x by multiplying both sides by (12 + x) to get:

48 + 5x = 4.995(12 + x)

48 + 5x = 59.94 + 4.995x

5x - 4.995x = 59.94 - 48

0.005x = 11.94

Dividing both sides by 0.005 then gives:

x = 2388

So you would need to add an additional 2388 surveys, all of which would have to be scored as a 5, in order to raise the average to 4.995, which would be 5.00 if you rounded off to two decimal places.

I hope this helps. Please feel free to ask if you have any additional questions about this.

Thanks,

Ryan