Question

Math

Posted 4 months ago

```
You have found the following ages (in years) of all 4 bears at your local zoo:
$5,4,6,39$
What is the average age of the bears at your zoo? What is the variance? Round your answers to the nearest tenth.
Average age:
$\square$ years old
Variance:
$\square$ years $^{2}$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Calculate the mean age of the bears by adding all the ages and dividing by the number of bears

step 2

Mean age = \frac{5 + 4 + 6 + 39}{4} = \frac{54}{4} = 13.5 \text{ years old}

step 3

Calculate the variance of the ages by finding the average of the squared differences from the mean

step 4

Variance = \frac{(5-13.5)^2 + (4-13.5)^2 + (6-13.5)^2 + (39-13.5)^2}{4} = \frac{72.25 + 90.25 + 56.25 + 650.25}{4} = \frac{869}{4} \approx 217.25 \text{ years}^2

step 5

Round the variance to the nearest tenth

step 6

Variance \approx 217.3 \text{ years}^2

[1] Answer

Average age: 13.5 years old

Variance: 217.3 years^2

Key Concept

Mean and Variance

Explanation

The mean is the average of a set of numbers, and the variance measures how much the numbers in the set deviate from the mean.

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