Which of the statements are correct

Question

I was trying to answer the question below.

Given the sets S1 = {2,3,5,8,9} and S2 = {3,4,5,6,7} which of the following statements are correct?

a. Median value and mean are 5 for both sets

b. For S2 the median value is equal to the mean value

c. S1 has a larger variance than S2

d. Both sets have the same variance

I tried solving it and it seems like both b and c are correct. The problem is there can only be one correct answer. Can someone check to see if they can answer the question or tell me if there is an error in the question.

Answer 1

You need to start by finding means, medians, and variances of the two samples. I have done this using R.

S1 = c(2,3,5,8,9) 
summary(S1); var(S1)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    2.0     3.0     5.0     5.4     8.0     9.0 
[1] 9.3

S2 = c(3,4,5,6,7) 
summary(S2); var(S2)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      3       4       5       5       6       7 
[1] 2.5

Answer 2

Contrary to your thinking, "which of the following statements are correct" allows several true statements.