Question
The table contains data on the cost of attending a play at 10 different theaters in the United States. Find the interquartile range for this data set. Explain what the interquartile range represents for this data set.
Cost of Attending a Play
Theater
Q
R
S
T
U
V
W
X
Y
Z
Cost ($)
60
63
43
45
30
51
62
40
38
41
Question content area bottom
Part 1
The interquartile range is
20.
Part 2
Explain what the interquartile range represents for this data set. Choose the correct answer below.
A.
The middle 50% of prices range from $40 to $60.
B.
The bottom 50% of prices range from $44 to $63.
C.
The top 25% of prices range from $30 to $40.
D.
The top 50% of prices range from $30 to $44.
Cost of Attending a Play
Theater
Q
R
S
T
U
V
W
X
Y
Z
Cost ($)
60
63
43
45
30
51
62
40
38
41
Question content area bottom
Part 1
The interquartile range is
20.
Part 2
Explain what the interquartile range represents for this data set. Choose the correct answer below.
A.
The middle 50% of prices range from $40 to $60.
B.
The bottom 50% of prices range from $44 to $63.
C.
The top 25% of prices range from $30 to $40.
D.
The top 50% of prices range from $30 to $44.
Answers
GPT-4o mini
To find the interquartile range (IQR) of the given data set on the cost of attending a play, we need to first organize the data in ascending order:
The sorted costs are:
- 30
- 38
- 40
- 41
- 43
- 45
- 51
- 60
- 62
- 63
Next, we determine the first quartile (Q1) and the third quartile (Q3):
1. **Finding Q1 (the median of the first half of the data)**:
- The first half of the data (lower half): 30, 38, 40, 41, 43
- The median of this group (Q1) is 40.
2. **Finding Q3 (the median of the second half of the data)**:
- The second half of the data (upper half): 45, 51, 60, 62, 63
- The median of this group (Q3) is 60.
3. **Calculating the IQR**:
- IQR = Q3 - Q1 = 60 - 40 = 20.
The interquartile range is thus 20, which means the middle 50% of the data falls within this range.
**Part 2 Explanation**:
The correct interpretation of the interquartile range (IQR) is:
**A. The middle 50% of prices range from $40 to $60.**
This means that the costs of attending a play for the middle 50% of observations (those between the first and third quartiles) are between $40 and $60.
The sorted costs are:
- 30
- 38
- 40
- 41
- 43
- 45
- 51
- 60
- 62
- 63
Next, we determine the first quartile (Q1) and the third quartile (Q3):
1. **Finding Q1 (the median of the first half of the data)**:
- The first half of the data (lower half): 30, 38, 40, 41, 43
- The median of this group (Q1) is 40.
2. **Finding Q3 (the median of the second half of the data)**:
- The second half of the data (upper half): 45, 51, 60, 62, 63
- The median of this group (Q3) is 60.
3. **Calculating the IQR**:
- IQR = Q3 - Q1 = 60 - 40 = 20.
The interquartile range is thus 20, which means the middle 50% of the data falls within this range.
**Part 2 Explanation**:
The correct interpretation of the interquartile range (IQR) is:
**A. The middle 50% of prices range from $40 to $60.**
This means that the costs of attending a play for the middle 50% of observations (those between the first and third quartiles) are between $40 and $60.