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
To find the standard deviation of a data set, you need to follow these steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Find the mean of the squared differences.
4. Take the square root of the mean of the squared differences to get the standard deviation.
Let's calculate it step by step:
Step 1: Find the mean
Mean = (51.8 + 53.6 + 54.7 + 51.9 + 49.3) / 5
Mean = 261.3 / 5
Mean = 52.26
Step 2: Subtract the mean and square the differences
(51.8 - 52.26)^2 = 0.2116
(53.6 - 52.26)^2 = 1.7924
(54.7 - 52.26)^2 = 5.9624
(51.9 - 52.26)^2 = 0.1296
(49.3 - 52.26)^2 = 8.7124
Step 3: Find the mean of squared differences
Mean of squared differences = (0.2116 + 1.7924 + 5.9624 + 0.1296 + 8.7124) / 5
Mean of squared differences = 16.8084 / 5
Mean of squared differences = 3.36168
Step 4: Take the square root of the mean of squared differences
Standard Deviation = √(3.36168)
Standard Deviation ≈ 1.8 (rounded to the nearest tenth)
Therefore, the standard deviation of the given data set, rounded to the nearest tenth, is approximately 1.8.