Question

A veterinarian weighed a sample of [6] puppies. Here are each of their weights (in kilograms): [1, 2, 7, 7, 10, 15]. The mean of these weights is [bar x = 7 kg]. What is the standard deviation? Round your answer to two decimal places.

Answer 1

The standard deviation of the puppy weights [1, 2, 7, 7, 10, 15] with a mean of 7 kg is approximately 4.72 kg.

Step-by-step explanation:

The student is asking for the calculation of the standard deviation of puppy weights. With the weights given as [1, 2, 7, 7, 10, 15] and the mean weight being 7 kg, we calculate the standard deviation by following these steps:

1. Subtract the mean from each individual weight to find the deviations.
2. Square each deviation.
3. Find the average of these squared deviations. This is the variance.
4. Take the square root of the variance to find the standard deviation.

Performing the calculations:

• The squared deviations are [(1-7)^2, (2-7)^2, (7-7)^2, (7-7)^2, (10-7)^2, (15-7)^2] which equals [36, 25, 0, 0, 9, 64].
• The variance is the average of these: (36 + 25 + 0 + 0 + 9 + 64) / 6 = 22.3333...
• The standard deviation is the square root of 22.3333..., which is approximately 4.72 when rounded to two decimal places.

Hence, the standard deviation of the puppy weights is 4.72 kg.