You have found the following ages (in years) of 5 porcupines. Those porcupines were randomly selected from the 26 porcupines at your local zoo:
$$
16,10,5,7,13
$$

Based on your sample, what is the average age of the porcupines? What is the standard deviation? Round your answers to the nearest tenth.

Average age:
$\square$ years old
Standard deviation:
$\square$ years

Question

You have found the following ages (in years) of 5 porcupines. Those porcupines were randomly selected from the 26 porcupines at your local zoo:
$$
16,10,5,7,13
$$

Based on your sample, what is the average age of the porcupines? What is the standard deviation? Round your answers to the nearest tenth.

Average age:
$\square$ years old
Standard deviation:
$\square$ years

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the mean age of the porcupines by adding all the ages together and dividing by the number of porcupines. ‖ ‖ step 2 ⋮ The sum of the ages is $16 + 10 + 5 + 7 + 13 = 51$. ‖ ‖ step 3 ⋮ There are 5 porcupines, so the mean age is $51 \div 5 = 10.2$. ‖ ‖ step 4 ⋮ Calculate the standard deviation by finding the square root of the variance. ‖ ‖ step 5 ⋮ The variance is the average of the squared differences from the mean. ‖ ‖ step 6 ⋮ The squared differences are $(16-10.2)^2$, $(10-10.2)^2$, $(5-10.2)^2$, $(7-10.2)^2$, and $(13-10.2)^2$. ‖ ‖ step 7 ⋮ Summing these and dividing by the number of porcupines minus 1 gives the variance: $\frac{(16-10.2)^2 + (10-10.2)^2 + (5-10.2)^2 + (7-10.2)^2 + (13-10.2)^2}{5-1} = \frac{197}{10}$. ‖ ‖ step 8 ⋮ The standard deviation is the square root of the variance: $\sqrt{\frac{197}{10}} \approx 4.4385$. ‖ ∻[1] Answer∻ ⚹ Average age: 10.2 years old ⚹ ⚹ Standard deviation: 4.4 years ⚹ ∻Key Concept∻ ⚹Mean and Standard Deviation⚹ ∻Explanation∻ ⚹The mean is the average of a set of numbers, and the standard deviation measures the amount of variation or dispersion from the mean.⚹◊What is the formula for calculating the standard deviation of a sample?⍭ Generate me a similar question◊

Sia