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.
55
60
42
42
27
49
61
45
37
40
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Part 1
The interquartile range is
  
enter your response here.

Answer 1

To find the interquartile range (IQR) of the given data set, we need to follow these steps:

1. **Order the data set from smallest to largest.**
2. **Find the first quartile (Q1), which is the median of the first half of the data.**
3. **Find the third quartile (Q3), which is the median of the second half of the data.**
4. **Calculate the interquartile range by subtracting Q1 from Q3 (IQR = Q3 - Q1).**

### Step 1: Order the data set

The given ticket prices are:
```
55, 60, 42, 42, 27, 49, 61, 45, 37, 40
```
Ordering them from smallest to largest:
```
27, 37, 40, 42, 42, 45, 49, 55, 60, 61
```

### Step 2: Find Q1 (the first quartile)

1. The ordered data set has 10 values.
2. To find Q1, we consider the lower half (first 5 values):
```
27, 37, 40, 42, 42
```
3. The median of these 5 values is the 3rd value:
```
Q1 = 40
```

### Step 3: Find Q3 (the third quartile)

1. For Q3, we consider the upper half (last 5 values):
```
45, 49, 55, 60, 61
```
2. The median of these 5 values is the 3rd value:
```
Q3 = 55
```

### Step 4: Calculate the interquartile range (IQR)

Now we can calculate the IQR:
\[
IQR = Q3 - Q1 = 55 - 40 = 15
\]

### Final Answer

The interquartile range is **15**.