The mean and standard deviation of $1,2,3,4,5,6$ are
- $\dfrac{7}{2},\sqrt{\dfrac{35}{12}}$
- $\dfrac{7}{3} ,\sqrt{3}$
- $3,3$
- $3,35/12$
Reveal answer
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Correct answer
Explanation
Mean = (1+2+3+4+5+6)/6 = 21/6 = 3.5 or 7/2. Variance = sum(x-mean)^2 / n = (6.25 + 2.25 + 0.25 + 0.25 + 2.25 + 6.25) / 6 = 17.5 / 6 = 35/12. Standard deviation is sqrt(35/12).
AI explanation
The mean of the six numbers is calculated as (1 + 2 + 3 + 4 + 5 + 6) divided by 6, which gives 7/2. Using the standard deviation formula, we find the variance by calculating the average of the squared deviations from the mean, giving 1/6 times (25/4 + 9/4 + 1/4 + 1/4 + 9/4 + 25/4). This simplifies to 1/6 times 70/4, resulting in a variance of 35/12, so the standard deviation is the square root of 35/12.