Question

for which set of numbers do the mean, median, and mode all have the same value?
1, 1, 2, 5, 6
2, 2, 2, 2, 4
1, 3, 3, 3, 5
1, 1, 1, 2, 5

Explanation:

Step1: Recall definitions

Mean is sum of numbers divided by count. Median is middle - number when ordered. Mode is most frequent number.

Step2: Check set 1,1,2,5,6

Mean: $\frac{1 + 1+2 + 5+6}{5}=\frac{15}{5}=3$. Median: 2. Mode: 1. They are not equal.

Step3: Check set 2,2,2,2,4

Mean: $\frac{2 + 2+2 + 2+4}{5}=\frac{12}{5}=2.4$. Median: 2. Mode: 2. They are not equal.

Step4: Check set 1,3,3,3,5

Mean: $\frac{1+3 + 3+3+5}{5}=\frac{15}{5}=3$. Median: 3. Mode: 3. They are equal.

Step5: Check set 1,1,1,2,5

Mean: $\frac{1+1 + 1+2+5}{5}=\frac{10}{5}=2$. Median: 1. Mode: 1. They are not equal.

Answer:

1,3,3,3,5