A set of 100 data points yields an average x̅  = 9 and a standard deviation σ_x = 4. The error in the estimated mean is closest to

Correct option is B

Given:

• Total number of data points, n = 100,
• Average (mean), x̅ = 9,
• Standard deviation, σ_x = 4,
• Find the error in the estimated mean.

Solution:

1. Formula for the error in the mean:
   The error in the estimated mean is calculated as:
   Error = Standard deviation (σ_x) / Square root of the number of data points (√n).

2. Substitute the given values:

   • Standard deviation (σ_x) = 4,
   • Total data points (n) = 100,
   • Square root of n = √100 = 10.

   Error = 4 / 10 = 0.4.

3. Interpretation:
   The error in the estimated mean is small because the number of data points is large, reducing uncertainty in the mean estimate.

Conclusion:
The error in the estimated mean is (b) 0.4.