A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one particular customer for the past 20 months. Use the given data to answer parts​ (a) and​ (b).

327327

456456

498498

396396

505505
 
350350

506506

349349

342342

320320

530530

462462

430430

414414

465465

552552

463463

439439

358358

363363

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Part 1

​(a) Determine the standard deviation and interquartile range of the data.

sequals=enter your response here 

​(Round to two decimal places as​ needed.)

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.

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one particular customer for the past 20 months. Use the given data to answer parts​ (a) and​ (b).

327, 456, 498, 396, 505, 350, 506, 349, 342, 320, 530, 462, 430, 414, 465, 552, 463, 439, 358, 363

Part 1​ (a) Determine the standard deviation and interquartile range of the data.

Determine the standard deviation and interquartile range for a customer's monthly phone usage data over 20 months. This solution covers key statistical concepts such as standard deviation and IQR, with detailed steps for calculation. Suitable for students in Grades 9-12.

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