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

Determine the interquartile range of the data.

337
452
513
418
448
546
525
466
426
535
359
374
464
515
346
325
500
377
522
474

The standard deviation is 72.14.

To determine the interquartile range (IQR) of the data, follow these steps:

1. **Sort the data in ascending order**.
2. **Find the first quartile (Q1)**, which is the median of the lower half of the data.
3. **Find the third quartile (Q3)**, which is the median of the upper half of the data.
4. **Calculate the interquartile range** using the formula:

\[
IQR = Q3 - Q1
\]

### Step 1: Sort the data
Sorted dataTo determine the interquartile range (IQR) of the data, follow these steps:

1. **Sort the data in ascending order**.
2. **Find the first quartile (Q1)**, which is the median of the lower half of the data.
3. **Find the third quartile (Q3)**, which is the median of the upper half of the data.
4. **Calculate the interquartile range** using the formula:

\[
IQR = Q3 - Q1
\]

### Step 1: Sort the data
Sorted 
325, 337, 346, 359, 374, 377, 418, 426, 448, 452, 464, 466, 474, 500, 513, 515, 522, 525, 535, 546

### Step 2: Find the first quartile (Q1)
The first quartile (Q1) is the median of the lower half of the data, excluding the overall median if the number of data points is odd.

Lower half:
325, 337, 346, 359, 374, 377, 418, 426, 448, 452

Since there are 10 data points, the median is the average of the 5th and 6th numbers:

\[
Q1 = \frac{374 + 377}{2} = 375.5
\]

### Step 3: Find the third quartile (Q3)
The third quartile (Q3) is the median of the upper half of the data.

Upper half:
464, 466, 474, 500, 513, 515, 522, 525, 535, 546

The median is the average of the 5th and 6th numbers:

\[
Q3 = \frac{513 + 515}{2} = 514
\]

### Step 4: Calculate the interquartile range (IQR)
Now, calculate the IQR:

\[
IQR = Q3 - Q1 = 514 - 375.5 = 138.5
\]

Thus, the interquartile range is **138.5**.

### Would you like more details or have any questions?

#### Related Questions:
1. How is the standard deviation (72.14) used to measure data spread?
2. What can the interquartile range tell us about this data set's variability?
3. How does the IQR compare to the range and standard deviation?
4. Can we identify any outliers using the IQR?
5. What does a high IQR indicate about the data?

#### Tip:
The IQR is useful for identifying outliers and understanding data variability, especially when dealing with skewed distributions.

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. Determine the interquartile range of the data. 337, 452, 513, 418, 448, 546, 525, 466, 426, 535, 359, 374, 464, 515, 346, 325, 500, 377, 522, 474. The standard deviation is 72.14.

Learn how to determine the interquartile range (IQR) of monthly phone usage data for a particular customer over 20 months. This example walks you through sorting the data, finding the first quartile (Q1), the third quartile (Q3), and calculating the IQR. The data's standard deviation is 72.14, adding context to the spread and variability.

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