Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To solve this question, we need to identify which formula correctly represents the standard deviation of a sample data set.
1. The formula for the sample standard deviation is:
[tex]\[ s = \sqrt{\frac{\left(x_1 - \bar{x}\right)^2 + \left(x_2 - \bar{x}\right)^2 + \ldots + \left(x_n - \bar{x}\right)^2}{n-1}} \][/tex]
2. The second formula given:
[tex]\[ \sigma^2 = \frac{\left(x_1 - \mu\right)^2 + \left(x_2 - \mu\right)^2 + \ldots + \left(x_N - \mu\right)^2}{N} \][/tex]
represents the variance of a population and not the sample standard deviation.
3. The third formula:
[tex]\[ \sigma = \sqrt{\frac{\left(x_1 - \mu\right)^2 + \left(x_2 - \mu\right)^2 + \ldots + \left(x_N - \mu\right)^2}{N}} \][/tex]
is the formula for the population standard deviation.
4. The fourth formula:
[tex]\[ s = \frac{\left(x_1 - \bar{x}\right)^2 + \left(x_2 - \bar{x}\right)^2 + \ldots + \left(x_n - \bar{x}\right)^2}{n-1} \][/tex]
is incorrect because it lacks the square root which is necessary for calculating the standard deviation (it resembles the sample variance formula).
Therefore, the formula used to calculate the standard deviation of sample data is:
[tex]\[ s = \sqrt{\frac{\left(x_1 - \bar{x}\right)^2 + \left(x_2 - \bar{x}\right)^2 + \ldots + \left(x_n - \bar{x}\right)^2}{n-1}} \][/tex]
1. The formula for the sample standard deviation is:
[tex]\[ s = \sqrt{\frac{\left(x_1 - \bar{x}\right)^2 + \left(x_2 - \bar{x}\right)^2 + \ldots + \left(x_n - \bar{x}\right)^2}{n-1}} \][/tex]
2. The second formula given:
[tex]\[ \sigma^2 = \frac{\left(x_1 - \mu\right)^2 + \left(x_2 - \mu\right)^2 + \ldots + \left(x_N - \mu\right)^2}{N} \][/tex]
represents the variance of a population and not the sample standard deviation.
3. The third formula:
[tex]\[ \sigma = \sqrt{\frac{\left(x_1 - \mu\right)^2 + \left(x_2 - \mu\right)^2 + \ldots + \left(x_N - \mu\right)^2}{N}} \][/tex]
is the formula for the population standard deviation.
4. The fourth formula:
[tex]\[ s = \frac{\left(x_1 - \bar{x}\right)^2 + \left(x_2 - \bar{x}\right)^2 + \ldots + \left(x_n - \bar{x}\right)^2}{n-1} \][/tex]
is incorrect because it lacks the square root which is necessary for calculating the standard deviation (it resembles the sample variance formula).
Therefore, the formula used to calculate the standard deviation of sample data is:
[tex]\[ s = \sqrt{\frac{\left(x_1 - \bar{x}\right)^2 + \left(x_2 - \bar{x}\right)^2 + \ldots + \left(x_n - \bar{x}\right)^2}{n-1}} \][/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.