Given the data set $5,7,9,10,14$, what is the value of the standard error of the mean for this sample?

• A. $1.43$
• B. $2.24$
• C. $4.00$
• D. $3.16$

Answer: (A)

Verified step by step guidance

1. First, calculate the sample mean \( \bar{x} \) by summing all the data points and dividing by the number of data points. For the data set 5, 7, 9, 10, and 14, the formula is: \[ \bar{x} = \frac{5 + 7 + 9 + 10 + 14}{5} \]
2. Next, find the deviations of each data point from the mean by subtracting the mean from each value. Then square each of these deviations to get squared differences.
3. Calculate the sample variance \( s^2 \) by summing all the squared differences and dividing by \( n - 1 \), where \( n \) is the sample size (number of data points). The formula is: \[ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} \]
4. Find the sample standard deviation \( s \) by taking the square root of the sample variance: \[ s = \sqrt{s^2} \]
5. Finally, calculate the standard error of the mean (SEM) by dividing the sample standard deviation by the square root of the sample size: \[ SEM = \frac{s}{\sqrt{n}} \]