Let's solve each part of this question step-by-step for the data provided:

The data points given are: $x = [17.4, 21.7, 11, 26.1, 7]$

Step 1: Find the Mean

The mean $\bar{x}$ is calculated as follows: $\bar{x} = \frac{\sum x}{n}$ where $n = 5$.

Calculating: $\bar{x} = \frac{17.4 + 21.7 + 11 + 26.1 + 7}{5} = \frac{83.2}{5} = 16.64$

So, the mean is 16.64.

Step 2: Find the Median

To find the median, we first arrange the data in ascending order: $[7, 11, 17.4, 21.7, 26.1]$

Since there are 5 values (an odd number), the median is the middle value: $\text{Median} = 17.4$

Thus, the median is 17.4.

Step 3: Find the Sample Standard Deviation

The sample standard deviation $s$ is calculated using: $s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}}$

1. Calculate each deviation from the mean, square it, and sum these squared deviations:

   • For $x = 17.4$: $(17.4 - 16.64)^2 = 0.5776$
   • For $x = 21.7$: $(21.7 - 16.64)^2 = 25.7284$
   • For $x = 11$: $(11 - 16.64)^2 = 31.8096$
   • For $x = 26.1$: $(26.1 - 16.64)^2 = 89.7796$
   • For $x = 7$: $(7 - 16.64)^2 = 92.9296$

2. Sum these values: $\sum (x - \bar{x})^2 = 0.5776 + 25.7284 + 31.8096 + 89.7796 + 92.9296 = 240.8248$

3. Divide by $n - 1 = 4$: $\frac{240.8248}{4} = 60.2062$

4. Take the square root: $s = \sqrt{60.2062} \approx 7.76$

Thus, the sample standard deviation is approximately 7.76.

Summary of Answers:

• Mean: 16.64
• Median: 17.4
• Sample Standard Deviation: 7.76

Would you like more details on any of these calculations, or do you have further questions?

Here are five related questions to deepen understanding:

1. What is the difference between sample standard deviation and population standard deviation?
2. How would the mean change if we added a new data point of 15?
3. How can we interpret the standard deviation in the context of this data set?
4. What would be the median if there was an even number of data points?
5. How does outlier data impact the mean and standard deviation?

Tip: For data sets with outliers, the median often provides a better measure of central tendency than the mean.