To determine the standard deviation and the interquartile range (IQR) of the data, we need to follow these steps:

1. Standard Deviation:

The standard deviation $s$ is calculated using the formula:

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

Where:

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

2. Interquartile Range (IQR):

The IQR is the difference between the third quartile $Q_3$ and the first quartile $Q_1$:

$\text{IQR} = Q_3 - Q_1$

Given Data:

The monthly phone usage (in minutes) for 20 months is: $327, 456, 498, 396, 505, 350, 506, 349, 342, 320, 530, 462, 430, 414, 465, 552, 463, 439, 358, 363$

Let me compute both the standard deviation and IQR.The standard deviation of the data is approximately $72.26$ minutes, and the interquartile range (IQR) is $117.25$ minutes.

Would you like a detailed explanation of how these values were computed, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. How is the mean value calculated for this data set?
2. What is the significance of standard deviation in analyzing data variability?
3. How do the quartiles relate to the median in a data set?
4. Can you calculate the variance from the standard deviation?
5. How would outliers in the data affect the standard deviation and IQR?

Tip: The IQR is a robust measure of variability, as it is not influenced by extreme values, unlike the standard deviation.