Final answer:
The standard deviation of the puppies' weights is calculated by finding the variance and taking its square root, resulting in a standard deviation of 5.18 kg.
Step-by-step explanation:
To calculate the standard deviation of the puppies' weights, we first need to find the variance. The variance is the average of the squared differences from the mean. Here are the steps to calculate the standard deviation:
- Calculate the mean of the weights. The mean (\(\overline{x}\)) is given as 7 kg.
- Subtract the mean from each weight and square the result. The squared differences are (1-7)^2, (2-7)^2, (7-7)^2, (7-7)^2, (10-7)^2, and (15-7)^2.
- Find the sum of these squared differences.
- Divide this sum by the number of weights (6) minus 1 to get the variance. This subtracting 1 is for the sample variance calculation.
- Take the square root of the variance to get the standard deviation.
Performing the calculations:
- (1-7)² = 36
- (2-7)² = 25
- (7-7)²= 0
- (7-7)²2 = 0
- (10-7)²2 = 9
- (15-7)²2 = 64
Sum of squared differences = 36 + 25 + 0 + 0 + 9 + 64 = 134
Variance = 134 / (6 - 1) = 134 / 5 = 26.8
Standard Deviation (\(s\)) = \(\sqrt{26.8}\) = 5.18 (rounded to two decimal places)
Therefore, the standard deviation of the puppies' weights is 5.18 kg.