Question

The table contains data on the admission price​ (in dollars) for​ one-day tickets to 10 theme parks in the United States. Find the interquartile range for this data set.
59
65
44
45
28
49
61
40
39
40
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Part 1
The interquartile range is
  
enter your response here.

Answer 1

To find the interquartile range (IQR), we'll follow these steps:

1. **Arrange the data in ascending order**.
2. **Find the first quartile (Q1)**, which is the median of the lower half of the data (the 25th percentile).
3. **Find the third quartile (Q3)**, which is the median of the upper half of the data (the 75th percentile).
4. **Calculate the IQR** by subtracting Q1 from Q3 (IQR = Q3 - Q1).

Let's start with your data:
59, 65, 44, 45, 28, 49, 61, 40, 39, 40

### Step 1: Arrange the Data

Sorted data:
28, 39, 40, 40, 44, 45, 49, 59, 61, 65

### Step 2: Find Q1

The lower half of the data is:
28, 39, 40, 40, 44

To find Q1, we calculate the median of this lower half. Since there are 5 numbers, the median is the 3rd number:
Q1 = 40

### Step 3: Find Q3

The upper half of the data is:
45, 49, 59, 61, 65

To find Q3, we calculate the median of this upper half. Again, with 5 numbers, the median is the 3rd number:
Q3 = 59

### Step 4: Calculate the IQR

IQR = Q3 - Q1 = 59 - 40 = 19

So, the interquartile range (IQR) is **19**.