Question

You have found the following ages (in years) of 6 anteaters. Those anteaters were randomly selected from the 271 anteaters at your local zoo:

16, 12, 15, 10, 5, 7
Based on your sample, what is the standard deviation? Round your answers to the nearest tenth.

Answer 1

To find the standard deviation of the given ages, calculate the mean, deviations, squared deviations, mean squared deviation, and the square root of the mean squared deviation. The standard deviation of the ages is approximately 4.2 years.

Step-by-step explanation:

To find the standard deviation of the given ages, we can use the following steps:

1. Find the mean (average) of the ages.
2. Subtract the mean from each age to find the deviation.
3. Square each deviation.
4. Find the mean of the squared deviations.
5. Take the square root of the mean squared deviation to get the standard deviation.

Applying these steps to the given ages:

1. Mean = (16 + 12 + 15 + 10 + 5 + 7) / 6 = 10.8
2. Deviations = (16 - 10.8), (12 - 10.8), (15 - 10.8), (10 - 10.8), (5 - 10.8), (7 - 10.8) = 5.2, 1.2, 4.2, -0.8, -5.8, -3.8
3. Squared deviations = 5.2^2, 1.2^2, 4.2^2, (-0.8)^2, (-5.8)^2, (-3.8)^2 = 27.04, 1.44, 17.64, 0.64, 33.64, 14.44
4. Mean squared deviation = (27.04 + 1.44 + 17.64 + 0.64 + 33.64 + 14.44) / 6 = 17.26
5. Standard deviation = sqrt(17.26) ≈ 4.2

Therefore, the standard deviation of the given ages is approximately 4.2 years.