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 numbers in increasing order
2, _, _, _, _*, _*, _, _, _, 7
The sum of the 10 numbers must be 10*3=30 which means the 8 blanks must sum to 21. The starred numbers form the median and so are either both 3 or a 2 and 4.
If the starred are a 2 and 4, the lowest possible sum to the ten numbers is 2*5+4*4+7=33. So we know
2, _, _, _, 3, 3, _, _, _, 7
The remaining blanks sum to 15 which is only possible with
2, 2, 2, 2, 3, 3, 3, 3, 3, 7
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Posted by Jer
on 2019-03-23 13:24:36 |
Solution
