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.

Option 1: 1.6
Option 2: 2.5
Option 3: 3.4
Option 4: 4.8

Answer 1

The standard deviation of the anteater ages is calculated to be 3.9 years when rounded to the nearest tenth. None of the given options exactly match the calculated value, which suggests there may be an error in the options provided.

Step-by-step explanation:

To find the standard deviation of the anteater ages, we will use the sample standard deviation formula, as we are working with a sample and not the entire population of anteaters. Here are the steps to calculate it:

1. Calculate the sample mean (average) by summing up the ages and dividing by the number of anteaters:
2. (16 + 12 + 15 + 10 + 5 + 7) / 6 = 65 / 6 = 10.833.
3. Subtract the mean from each age and square the result, then sum up these squared differences:
4. (16 - 10.833)^2 + (12 - 10.833)^2 + (15 - 10.833)^2 + (10 - 10.833)^2 + (5 - 10.833)^2 + (7 - 10.833)^2 = 74.833.
5. Divide the sum by the number of samples minus 1 (n-1):
6. 74.833 / (6 - 1) = 74.833 / 5 = 14.9666.
7. Finally, take the square root of the result to obtain the standard deviation:
8. √14.9666 = 3.869.

When rounded to the nearest tenth, the standard deviation is 3.9 years, which is not listed in the given options. It seems there might have been a slight error in the options provided as none of them exactly match the calculated value.