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Let X be a random variable representing a set of measurements of a particular quantity. Typically, the uncertainty in X is represented as $\bar X \pm \sigma_{\bar X}$ where $\bar X$ is the mean of X and $\sigma_{\bar X}$ is the standard deviation of the mean of X, both evaluated from a set of measurements for X. The uncertainty is a standard deviation, not an absolute limit for the possible values of X.

See my answer to Uncertainty in repetitive measurements on this exchange for more details. This reference provides details on how to evaluate the standard deviation of both the data and of the mean.

Regarding significant figures. See http://physchemreview.weebly.com/significant-figures--uncertainty.html#:~:text=SIGNIFICANT%20FIGURES%20%26%20UNCERTAINTY%201%20%20Zeros%20at,left%20of%20a%20small%20number%20are%20not%20 for details. Note: all zeros used for spacing the decimal point are not significant; for example, 6500 has two significant figures. The uncertainty must have the same number of decimals as the measurement. To avoid confusion, use scientific notation; $6.5 \times 10^3$. For the above example of the estimated mean, the rightmost digit reported for the mean should be uncertain and the digit just to the left should be certain. The standard deviation should express the uncertainty in the right most digit. For example, $\bar X \pm \sigma_{\bar X} = 10.50 \pm 0.04$.

Let X be a random variable representing a set of measurements of a particular quantity. Typically, the uncertainty in X is represented as $\bar X \pm \sigma_{\bar X}$ where $\bar X$ is the mean of X and $\sigma_{\bar X}$ is the standard deviation of the mean of X, both evaluated from a set of measurements for X. The uncertainty is a standard deviation, not an absolute limit for the possible values of X.

See my answer to Uncertainty in repetitive measurements on this exchange for more details. This reference provides details on how to evaluate the standard deviation of both the data and of the mean.

Regarding significant figures. To avoid confusion, use scientific notation. The rightmost digit reported for the measurement should be uncertain, and the digit just to the left should be certain. The uncertainty should express the uncertainty in the right most digit.

For example, the rightmost digit reported for the mean should be uncertain and the digit just to the left should be certain. The standard deviation should express the uncertainty in the rightmost digit. For example, $\bar X \pm \sigma_{\bar X} = 1.050 \times 10^1 \pm 4 \times 10^{-2}$.

See http://physchemreview.weebly.com/significant-figures--uncertainty.html#:~:text=SIGNIFICANT%20FIGURES%20%26%20UNCERTAINTY%201%20%20Zeros%20at,left%20of%20a%20small%20number%20are%20not%20 for details.

Let X be a random variable representing a set of measurements of a particular quantity. Typically, the uncertainty in X is represented as $\bar X \pm \sigma_{\bar X}$ where $\bar X$ is the mean of X and $\sigma_{\bar X}$ is the standard deviation of the mean of X, both evaluated from a set of measurements for X. The uncertainty is a standard deviation, not an absolute limit for the possible values of X.

See my answer to Uncertainty in repetitive measurements on this exchange for more details. This reference provides details on how to evaluate the standard deviation of both the data and of the mean.

Regarding significant figures. All zeros used for spacing the decimal point are not significant; for example 6500 has two significant figures. The uncertainty must have the same number of decimals as the measurement. For the above example of the estimated mean, the rightmost digit reported for the mean should be uncertain and the digit just to the left should be certain. The standard deviation should express the uncertainty in the right most digit. For example, $\bar X \pm \sigma_{\bar X} = 10.50 \pm 0.04$. See http://physchemreview.weebly.com/significant-figures--uncertainty.html#:~:text=SIGNIFICANT%20FIGURES%20%26%20UNCERTAINTY%201%20%20Zeros%20at,left%20of%20a%20small%20number%20are%20not%20significant for mred details.

Let X be a random variable representing a set of measurements of a particular quantity. Typically, the uncertainty in X is represented as $\bar X \pm \sigma_{\bar X}$ where $\bar X$ is the mean of X and $\sigma_{\bar X}$ is the standard deviation of the mean of X, both evaluated from a set of measurements for X. The uncertainty is a standard deviation, not an absolute limit for the possible values of X.

See my answer to Uncertainty in repetitive measurements on this exchange for more details. This reference provides details on how to evaluate the standard deviation of both the data and of the mean.

Regarding significant figures. See http://physchemreview.weebly.com/significant-figures--uncertainty.html#:~:text=SIGNIFICANT%20FIGURES%20%26%20UNCERTAINTY%201%20%20Zeros%20at,left%20of%20a%20small%20number%20are%20not%20 for details. Note: all zeros used for spacing the decimal point are not significant; for example, 6500 has two significant figures. The uncertainty must have the same number of decimals as the measurement. To avoid confusion, use scientific notation; $6.5 \times 10^3$. For the above example of the estimated mean, the rightmost digit reported for the mean should be uncertain and the digit just to the left should be certain. The standard deviation should express the uncertainty in the right most digit. For example, $\bar X \pm \sigma_{\bar X} = 10.50 \pm 0.04$.

Let X be a random variable representing a set of measurements of a particular quantity. Typically, the uncertainty in X is represented as $\bar X \pm \sigma_{\bar X}$ where $\bar X$ is the mean of X and $\sigma_{\bar X}$ is the standard deviation of the mean of X, both evaluated from a set of measurements for X. The uncertainty is a standard deviation, not an absolute limit for the possible values of X.

See my answer to Uncertainty in repetitive measurements on this exchange for more details. This reference provides details on how to evaluate the standard deviation of both the data and of the mean.

Regarding significant figures. As some say "the uncertainty must have the same number of decimals as the measurement". For the above example of the estimated mean, the rightmost digit reported for the mean should be uncertain and the digit just to the left should be certain. The standard deviation should express the uncertainty in the right most digit. For example, $\bar X \pm \sigma_{\bar X} = 10.50 \pm 0.04$.

Let X be a random variable representing a set of measurements of a particular quantity. Typically, the uncertainty in X is represented as $\bar X \pm \sigma_{\bar X}$ where $\bar X$ is the mean of X and $\sigma_{\bar X}$ is the standard deviation of the mean of X, both evaluated from a set of measurements for X. The uncertainty is a standard deviation, not an absolute limit for the possible values of X.

See my answer to Uncertainty in repetitive measurements on this exchange for more details. This reference provides details on how to evaluate the standard deviation of both the data and of the mean.

Regarding significant figures. All zeros used for spacing the decimal point are not significant; for example 6500 has two significant figures. The uncertainty must have the same number of decimals as the measurement. For the above example of the estimated mean, the rightmost digit reported for the mean should be uncertain and the digit just to the left should be certain. The standard deviation should express the uncertainty in the right most digit. For example, $\bar X \pm \sigma_{\bar X} = 10.50 \pm 0.04$. See http://physchemreview.weebly.com/significant-figures--uncertainty.html#:~:text=SIGNIFICANT%20FIGURES%20%26%20UNCERTAINTY%201%20%20Zeros%20at,left%20of%20a%20small%20number%20are%20not%20significant for mred details.