326
347
412
340
341
422
551
514
473
449
438
399
327
501
503
512
505
350
392
442A 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).
326
347
412
340
341
 
422
551
514
473
449
438
399
327
501
503
512
505
350
392
442
Question content area bottom
Part 1
​(a) Determine the standard deviation and interquartile range of the data. s=

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

### Part 1: **Standard Deviation**
The formula for the sample standard deviation \( s \) is:

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

Where:
- \( x_i \) represents each data point.
- \( \bar{x} \) is the mean of the data.
- \( n \) is the total number of data points (in this case, \( n = 20 \)).

### Part 2: **Interquartile Range (IQR)**
The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1):

\[
IQR = Q3 - Q1
\]

Let me calculate the standard deviation and IQR for the given data.

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). 326, 347, 412, 340, 341, 422, 551, 514, 473, 449, 438, 399, 327, 501, 503, 512, 505, 350, 392, 442. (a) Determine the standard deviation and interquartile range of the data.

Learn how to calculate the standard deviation and interquartile range (IQR) of a customer's monthly phone usage data. This problem includes a detailed explanation of key statistical measures, including the standard deviation formula and interquartile range (IQR) for data spread. Suitable for students in Grades 10-12.

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