This paper discusses the implementation and interpretation of the analysis scheme in the ensemble Kalman filter (EnKF). It highlights that observations must be treated as random variables at the analysis steps, which involves adding random perturbations to the observations to generate an ensemble of observations. This modification ensures that the updated ensemble has the correct variance, addressing a common issue where the variance is too low without this step. The paper also explains that the covariance of the ensemble of model states can be interpreted as the prediction error covariance, provided the ensemble size is sufficient. The analysis scheme is compared with the standard Kalman filter, showing that the EnKF can be interpreted as a purely statistical Monte Carlo method. The paper includes a detailed derivation of the analysis step and a comparison with the standard Kalman filter, demonstrating the consistency of the modified EnKF. An example is provided to illustrate the differences between the original and modified EnKF, confirming the effectiveness of the proposed modification. The paper concludes by emphasizing the importance of treating observations as random variables and the practical implications for existing EnKF applications.This paper discusses the implementation and interpretation of the analysis scheme in the ensemble Kalman filter (EnKF). It highlights that observations must be treated as random variables at the analysis steps, which involves adding random perturbations to the observations to generate an ensemble of observations. This modification ensures that the updated ensemble has the correct variance, addressing a common issue where the variance is too low without this step. The paper also explains that the covariance of the ensemble of model states can be interpreted as the prediction error covariance, provided the ensemble size is sufficient. The analysis scheme is compared with the standard Kalman filter, showing that the EnKF can be interpreted as a purely statistical Monte Carlo method. The paper includes a detailed derivation of the analysis step and a comparison with the standard Kalman filter, demonstrating the consistency of the modified EnKF. An example is provided to illustrate the differences between the original and modified EnKF, confirming the effectiveness of the proposed modification. The paper concludes by emphasizing the importance of treating observations as random variables and the practical implications for existing EnKF applications.