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.