a student recorded the ages of 4 zebras. The ages are 2, 9, 14, 15. The mean is 10....

1. Calculate the deviation of each age from the mean: The mean age is given as $\bar{x} = 10$ years. The deviations are calculated by subtracting the mean from each age.
- For age 2: $2 - 10 = -8$
- For age 9: $9 - 10 = -1$
- For age 14: $14 - 10 = 4$
- For age 15: $15 - 10 = 5$

2. Square each deviation: Squaring the deviations makes them all positive and emphasizes larger differences.
- $(-8)^2 = 64$
- $(-1)^2 = 1$
- $4^2 = 16$
- $5^2 = 25$

3. Sum the squared deviations: Add up all the squared deviations.
$64 + 1 + 16 + 25 = 106$

4. Calculate the variance: For a sample standard deviation, we divide the sum of squared deviations by $n-1$, where $n$ is the number of data points. Here, $n=4$.
Variance ($s^2$) = $\frac{\sum (x_i - \bar{x})^2}{n-1} = \frac{106}{4-1} = \frac{106}{3} \approx 35.3333$

5. Calculate the standard deviation: The standard deviation is the square root of the variance.
Standard Deviation ($s$) = $\sqrt{\text{Variance}} = \sqrt{\frac{106}{3}} \approx \sqrt{35.3333} \approx 5.9442$

6. Round the answer: Round the standard deviation to two decimal places as requested.
$5.9442 \approx 5.94$