Questions: Makis wants to calculate the standard error of the sample mean for this set of data. What is the standard error for this set of data?

Solution Steps

To find the mean \( \mu \) of the data, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

For the given data, the calculation is:

\[ \mu = \frac{101}{10} = 10.1 \]

Next, we calculate the variance \( \sigma^2 \) using the formula for sample variance:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} \]

After performing the calculations, we find:

\[ \sigma^2 = 3.66 \]

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{3.66} = 1.91 \]

Finally, we calculate the standard error (SE) of the sample mean using the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} \]

Where \( n \) is the number of observations. Thus, we have:

\[ SE = \frac{1.91}{\sqrt{10}} \approx 0.6 \]

Final Answer