A class of 10 students was asked for the number of days each week that they play video games. They each gave an integer answer. The smallest answer is 2 and the largest answer is 7. Teresa the Teacher realized that the mean, mode and median are all equal to 3.
What are these 10 numbers?
The integers provided by the 10 students in increasing order are as follows:
2 () () () # # () () () 7
Since the mean is 3, it follows that the total of the numbers given by the students is 10*3=30
Since the median is 3, it follows that the hashed numbers are:
-> Either: 2, and 4
-> Or: 3, and 3
In the former CASE, we observe that none of the numbers can be 3. This contradicts the given condition that the mode is equal to 3.
Therefore, the correct assignment is: 3, and 3 -- so that, we have the 10 numbers as follows:
2 () () () 3 3 () () () 7
Then, the numbers in blank spaces must add up to: 30 - (2+7+3+3) = 15
By way of trial and error, we observe that this is achieved by precisely three 2s and three 3s, i.e., 2*3 +3*3 = 15
Consequently, the required 10 number provided by the students are:
--> 2, 2, 2, 2, 3, 3, 3, 3, 3, 7
Edited on June 29, 2022, 2:04 am
Puzzle Solution
