The value in the data set is 4,5,6 and the total observations is 1,3,1.
Calculate the standard deviation of the data set. Round the answer to the nearest hundredth.
A. 0.71
B. 0.50
C. 0.25
D. 5.00
To calculate the standard deviation, first we need to find the mean of the data set.
Mean = (4*1 + 5*3 + 6*1) / (1+3+1)
Mean = (4 + 15 + 6) / 5
Mean = 25 / 5
Mean = 5
Next, calculate the variance by finding the squared difference between each data point and the mean, then taking the average of those squared differences.
Variance = ((4-5)^2 * 1 + (5-5)^2 * 3 + (6-5)^2 * 1) / (1+3+1)
Variance = (1*1 + 0*3 + 1*1) / 5
Variance = (1 + 1) / 5
Variance = 2 / 5
Variance = 0.4
Finally, the standard deviation is the square root of the variance.
Standard Deviation = √0.4
Standard Deviation ≈ 0.63
Therefore, the standard deviation of the data set is 0.63. The closest answer choice is A. 0.71.