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)

var1
339
484
524
548
517
403
551
387
487
466
418
448
453
553
424
414
454
485
405
462
Determine the standard deviation and interquartile range of the data.
sequals
  
enter your response here ​(Round to two decimal places as​ needed.)

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.

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 determine the standard deviation and interquartile range of the data.

Learn how to calculate the standard deviation and interquartile range (IQR) of a dataset representing the monthly phone usage in minutes over 20 months. This problem includes key statistical concepts and is suitable for students in Grades 9-12.

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