Shifting Data Sample annual salaries (in thou...

Question

Shifting Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.

40 35 49 53 38 39 40

37 49 34 38 43 47 35

a. Find the sample mean and the sample standard deviation.

Accepted Answer

Hello everyone. Let's take a look at this question together. A company's quarterly bonuses in thousands of dollars for a group of employees are as follows 22, 25, 28, 31, 24, 27, 29, 23, 30, 26, 25, and 28. What are the sample mean and sample standard deviation for the data set. So in order to solve this question, we have to recall how to find the sample mean and the sample standard deviation so that we can determine them for our data set of a company's quarterly bonuses in thousands of dollars. And so the first step in solving this problem is to calculate the sample mean. Which we know that the sample mean X bar is given by the following formula of X is equal to 1 divided by N multiplied by the sum of all Xi from I equals 1 ton multiplied by Xi, where we know that N is the number of data points which looking at our. data we know is equal to 12, and the total sum of all of the data values is equal to 318. So then plugging in the values into our sample mean formula X bar is equal to 318 divided by 12, which is equal to 26.5. So our sample mean is 26.5. Then we calculate the sample standard deviation using the following formula for the sample standard deviation, where first we can compute the square deviations from the mean, which is 26.5. Giving us the following data table of our x values, our X minus X bar values, and the square of our X minus X bar values, and substituting the values from the data table into our formula for the sample standard deviation, we have the square root of 87 divided by 11, which is approximately 2.81. Therefore, the value for the sample standard deviation is equal to 2.81. And since the company's quarterly bonuses are in thousands of dollars, we know that the sample mean is equal to $26,500 and the sample standard deviation is equal to $2810 which looking at our answer choices, we can identify is answer choice D. So answer choice D is the correct answer. I hope you found this video to be helpful. Thank you and goodbye.

��app

Shifting Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.
40 35 49 53 38 39 40
37 49 34 38 43 47 35

a. Find the sample mean and the sample standard deviation.

Key Concepts

Sample Mean

Sample Standard Deviation

Data Shifting

Watch next

����app

Shifting Data Sample annual salaries (in thousands of dollars) for employees at a company are listed.40 35 49 53 38 39 4037 49 34 38 43 47 35a. Find the sample mean and the sample standard deviation.