Final answer:
The standard deviation for the dataset {7, 2, 7, 2, 7} is calculated by determining the mean, finding the squared deviations from mean, calculating the variance, and then the square root of variance, resulting in a standard deviation of approximately 2.4.
Step-by-step explanation:
To find the standard deviation for the group of data items {7, 2, 7, 2, 7}, we first need to calculate the mean (average) of these numbers. To do this, we add up all the numbers and divide by the number of items in the dataset.
Mean = (7 + 2 + 7 + 2 + 7) / 5 = 25 / 5 = 5
Next, we calculate each data point's deviation from the mean (difference between the data point and the mean), then square those deviations:
- (7 - 5)^2 = 4
- (2 - 5)^2 = 9
- (7 - 5)^2 = 4
- (2 - 5)^2 = 9
- (7 - 5)^2 = 4
Add up the squared deviations:
Total squared deviations = 4 + 9 + 4 + 9 + 4 = 30
To calculate the variance, we divide by the number of data points if it's a population or by the number of data points minus one if it's a sample. In this case, we will assume it is a population. Thus, variance = 30 / 5 = 6.
Lastly, the standard deviation is the square root of the variance:
Standard Deviation = sqrt(6) ≈ 2.4495
Therefore, the standard deviation of the dataset {7, 2, 7, 2, 7} is approximately 2.4 when rounded to the nearest tenth.