averages, median and mode

Question

Federal law requires that room temperature in long-term care facilities does not exceed maximum of 84?when the humidity is below 60% after two readings of 83? and 86? in one day, what must the third required reading be to average 84?? 

Answer 1

Lynn, this problem is about finding out what other number must be present so that the average is 84. To do this, you need to understand how to calculate for average.

 

The average is found by adding all of the numbers and then dividing the sum by how many numbers were added together. The problem gave you two readings and asked you for what the third reading should be. This means that there are three numbers in total that you must add together. Using x as the third reading, the equation for average would be:

(83+86+x)/3 =84

 

Let's solve for x by isolating it:

 

(83+86+x)/3 •3=84•3

83+86-83+x= 252-83

86-86+x= 169-86

x= 83

 

The third reading would be 83. Double check the math: Does (83+86+83)/3 =84?

Answer 2

An average is computed by summing all of the values given and then dividing the sum by the number of values. Example:

 

If I have the numbers 4, 5, 6, the sum would be 15 and the number of values would be 3. The average would than be 15 divided by 3, which equals 5.

 

In your problem, you are given the average. Your job is to find out what three numbers when added together and then divided by 3 equals the given average.

 

We have:

  

        83 + 86 + an unknown value        

84 = ---------------------------------

                           3

 

The first step is to multiply both sides by 3 to eliminate the fraction on the right side of the equal sign.

 

84 * 3 = 83 + 86 + an unknown value (1)

 

Multiply 84 * 3 giving 252

 

Add 83 + 86 giving 169

 

Replacing these values in (1) above:

 

252 = 169 + an unknown value

 

To find the unknown value, subtract 169 from both sides of the equation giving:

 

252 - 169 = 169 - 169 + an unknown value

 

This gives:

 

83 = the unknown value

 

We can check this by calculating the average for the values 83, 86, 83.

 

                   83 + 86 + 83

A(verage) = ---------------

                           3

 

This gives:

 

                   252
A(verage) = ---- = 84
                    3

 

Questions?