To calculate the standard deviation and the interquartile range (IQR) of the given data, we will follow these steps:

Step 1: Organize the data

The given data is:

$339, 484, 524, 548, 517, 403, 551, 387, 487, 466, 418, 448, 453, 553, 424, 414, 454, 485, 405, 462$

Step 2: Standard Deviation Calculation

The formula for the standard deviation $s$ is:

$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$ Where:

• $n$ is the number of data points
• $\bar{x}$ is the mean (average) of the data points
• $x_i$ represents each data point

Step 3: Interquartile Range (IQR) Calculation

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1): $IQR = Q3 - Q1$

Let me perform these calculations for you.The standard deviation of the data is approximately 58.77 and the interquartile range (IQR) is 77.5.

Would you like a more detailed explanation or any additional information on this? Here are 5 related questions:

1. How is the standard deviation used to measure data variability?
2. What are quartiles, and how do they relate to the interquartile range?
3. How can we interpret the interquartile range in practical scenarios?
4. How is the sample standard deviation different from population standard deviation?
5. Can outliers significantly affect the standard deviation and IQR?

Tip: The standard deviation provides a measure of spread, while the interquartile range focuses on the middle 50% of the data, making it more resistant to outliers.