What is the standard deviation of the following data set rounded to the nearest tenth?
51.8, 53.6, 54.7, 51.9, 49.3
A) 1.9***
B) 3.3
C) 1.8
D) 3.4
I did not get that, show me your work to see where you went wrong.
To find the standard deviation of a data set, you would need to follow these steps:
Step 1: Calculate the mean of the data set. Add up all the numbers in the data set and divide the sum by the number of data points. In this case, there are 5 data points, so you would add up 51.8, 53.6, 54.7, 51.9, and 49.3, which equals 261.3. Then divide 261.3 by 5, which equals 52.26.
Step 2: Calculate the squared difference of each data point from the mean. Subtract the mean from each data point, and then square the result. For example, the squared difference of 51.8 from the mean (52.26) is (51.8 - 52.26)^2 = 0.2044. Repeat this calculation for every data point.
Step 3: Calculate the average of the squared differences. Add up all the squared differences from Step 2 and divide the sum by the number of data points. In this case, the sum of the squared differences is 0.2044 + 0.1864 + 3.0624 + 0.0064 + 5.2274 = 8.6870. Divide this sum by 5, which equals 1.7374.
Step 4: Take the square root of the average of the squared differences calculated in Step 3. In this case, the square root of 1.7374 is approximately 1.32.
Therefore, the standard deviation of the data set rounded to the nearest tenth is approximately 1.3. None of the answer choices provided match this result, so none of the answers are correct.