Final answer:
The standard deviation of the weights of 6 puppies is calculated by subtracting the mean from each weight, squaring the results, finding the sum and calculating the variance by dividing this sum by the number of puppies. The standard deviation is the square root of the variance, which in this case is approximately 4.72kg.
Step-by-step explanation:
You've been tasked with calculating the standard deviation of the weights of 6 puppies. The standard deviation is a measure of how spread out the numbers in a data set are. To find the standard deviation, you can follow these steps:
Calculate the mean of the data set (which has been provided as 7kg).
Subtract the mean from each of the weights to find the deviations.
Square each deviation to find the squared deviations.
Add up all the squared deviations.
Divide by the number of puppies to find the variance.
Take the square root of the variance to find the standard deviation.
Applying the steps to the provided data:
The mean is Överline x = 7kg.
The deviations are: -6, -5, 0, 0, 3, 8.
The squared deviations are: 36, 25, 0, 0, 9, 64.
The sum of squared deviations is: 36 + 25 + 0 + 0 + 9 + 64 = 134.
The variance is: 134 divided by 6 = 22.333.
The standard deviation is: the square root of 22.333 = 4.72kg (approx).
Therefore, the standard deviation of the puppies' weights is approximately 4.72kg.