To solve this, we calculate the mean, median, and sample standard deviation of the given dataset. The steps are as follows:

Data:

x = [14.8, 15.7, 25.6, 22.1, 12.9]

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1. Mean:

The formula for the mean is:

$\text{Mean} = \frac{\sum x_i}{n}$

$\text{Mean} = \frac{14.8 + 15.7 + 25.6 + 22.1 + 12.9}{5} = \frac{91.1}{5} = 18.22$

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2. Median:

To find the median, arrange the data in ascending order:

$[12.9, 14.8, 15.7, 22.1, 25.6]$

Since there is an odd number of data points ($n=5$), the median is the middle value:

$\text{Median} = 15.7$

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3. Sample Standard Deviation:

The formula for sample standard deviation is:

$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$

Steps:

1. Compute the deviations $(x_i - \bar{x})$, where $\bar{x} = 18.22$.
2. Square the deviations $(x_i - \bar{x})^2$.
3. Sum the squared deviations.
4. Divide by $n-1$, where $n=5$.
5. Take the square root.

$s = \sqrt{\frac{(14.8 - 18.22)^2 + (15.7 - 18.22)^2 + (25.6 - 18.22)^2 + (22.1 - 18.22)^2 + (12.9 - 18.22)^2}{5-1}}$

$s = \sqrt{\frac{(-3.42)^2 + (-2.52)^2 + (7.38)^2 + (3.88)^2 + (-5.32)^2}{4}}$

$s = \sqrt{\frac{11.70 + 6.35 + 54.46 + 15.05 + 28.30}{4}}$

$s = \sqrt{\frac{115.86}{4}} = \sqrt{28.96} = 5.38$

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Final Answers:

1. Mean: $18.22$
2. Median: $15.7$
3. Sample Standard Deviation: $5.38$

Let me know if you want further explanations!

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Related Questions:

1. How do you interpret the mean in this context?
2. What is the significance of the median for skewed datasets?
3. How does standard deviation measure data spread?
4. What would change in calculations if it were a population standard deviation?
5. How would adding an extra value affect the mean and standard deviation?

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Tip:

Always organize data in ascending order for median calculations and recheck arithmetic steps for accuracy.