my test scores

Question

Today I am supposed to tell my grades from my math tests, but I forgot my list. I do remember these facts about my scores. I had a 100. The mean. median. and mode for my set of test scores is 83. The range of my scores is 42. What are my five test scores?

Answer 1

Assuming that the highest score you can get on a single test is 100, since range = high - low, 42 = 100 - low, the lowest score was 58.  Since the mode is the most frequent score, there are either three 83's or two 83's.

 

 If there are three 83's, then the mean is (sum of scores)/5 = 81.4.  So, since the mean is 83, we can't have three scores of 83.  So, the five scores are 58, 100, 83, 83, and x.  

 

Mean = (58+100+83+83+x)/5 = 83

 

                             (324+x)/5 = 83

 

                                  324+x = 415

 

                                         x = 91

 

The scores are:  58, 83, 83, 91, 100

 

Answer 2

Let the test scores be I, J, K, L and M (in any order).

 

M=100         ["I had a 100"]

 

I = 58           ["The range ... is 42."  100-58=42]

 

["The mean ... is 83... my five test scores?]

    (58 + J + K + L + 100)/5 = 83

      (J+K+L+158)/5 = 83

      (J+K+L)= 257      [eq1]

 

["The ... mode ... is 83 ...]

     Let J=K=83          [eq2]   [note: the mode must be at least two of same value]

        J+K+L=257       [from eq1]

        83+83+L=257

              L = 91

 

The test scores are:    58, 83, 83, 91, 100   

        [note that the median (middle value of sorted list) is, in fact, 83 as stated]

 

Answer 3

I would say the test scores are:

 

mean = 83

 

range is 42

 

score of 100

 

  62, 66, 83, 100 104