Question : The arithmetic mean of the following numbers
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:
Option 1: 4
Option 2: 5
Option 3: 14
Option 4: 20
Correct Answer: 5
Solution :
Arithmetic mean or average
= $\frac{\text{Sum of the numbers}}{\text{Total count}}$
= $\frac{1+2+2+3+3+3+4+4+4+4+5+5+5+5+5+6+6+6+6+6+6+7+7+7+7+7+7+7}{28}$
= $\frac{1+2×2+3×3+4×4+5×5+6×6+7×7}{28}$
= $\frac{1+4+9+16+25+36+49}{28}$
= $\frac{140}{28}$
= $5$
Hence, the correct answer is 5.
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