It's important because it helps us understand how reliable our sample data is. A smaller standard error means our sample is likely a good representation of the population, while a larger standard error means more variability and less confidence in the sample's accuracy.

error bar means standard deviation of data

bad is B becuase its error bar is vey high and good is C because its error bar is not too high

good = c bad = b

we use the SEM when we are interested in the accuracy of the sample mean as an estimate of the population mean, especially in the context of hypothesis testing, confidence intervals, and other inferential statistics. The SD is used when we are interested in understanding the variability within the sample itself.

For example, if we're conducting an experiment and taking multiple measurements, the standard deviation can tell us how much our measurements for each individual trial vary. On the other hand, the standard error of the mean can tell us how much our overall estimate of the mean is likely to vary.

We use Standard Error (SE) instead of Standard Deviation (SD) when describing the variability of a sample statistic, like a mean, because SE accounts for the sample size and provides a more accurate estimate of the population parameter's uncertainty.

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Standard Deviation (SD): Measures the spread of individual data points within a single dataset. It tells you how much variation there is from the mean within that specific group. Standard Error of the Mean (SEM): Measures the expected variability of sample means around the true population mean. It tells you how much the sample mean is likely to differ from the population mean due to random sampling error.