Question
Problem
The data below represents the number of desks on each floor of Texter Corporate.
\[\qquad54,60,65,66,67,69,70,72,73,75,76\]
Which box plot correctly summarizes the data?
Choose 1 answer:
Choose 1 answer:
(Choice A) A horizontal boxplot is plotted along a horizontal axis marked from 50 to 80, in increments of 1. A left whisker extends from 54 to 67. The box extends from 67 to 73 and is divided into 2 parts by a vertical line segment at 70. The right whisker extends from 73 to 76. All values estimated.
A
A horizontal boxplot is plotted along a horizontal axis marked from 50 to 80, in increments of 1. A left whisker extends from 54 to 67. The box extends from 67 to 73 and is divided into 2 parts by a vertical line segment at 70. The right whisker extends from 73 to 76. All values estimated.
(Choice B) A horizontal boxplot is plotted along a horizontal axis marked from 50 to 80, in increments of 1. A left whisker extends from 54 to 65. The box extends from 65 to 73 and is divided into 2 parts by a vertical line segment at 69. The right whisker extends from 73 to 76. All values estimated.
B
A horizontal boxplot is plotted along a horizontal axis marked from 50 to 80, in increments of 1. A left whisker extends from 54 to 65. The box extends from 65 to 73 and is divided into 2 parts by a vertical line segment at 69. The right whisker extends from 73 to 76. All values estimated.
(Choice C) A horizontal boxplot is plotted along a horizontal axis marked from 50 to 80, in increments of 1. A left whisker extends from 54 to 67. The box extends from 67 to 72 and is divided into 2 parts by a vertical line segment at 70. The right whisker extends from 72 to 76. All values estimated.
C
A horizontal boxplot is plotted along a horizontal axis marked from 50 to 80, in increments of 1. A left whisker extends from 54 to 67. The box extends from 67 to 72 and is divided into 2 parts by a vertical line segment at 70. The right whisker extends from 72 to 76. All values estimated.
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Answers
GPT-4o mini
To determine which box plot correctly summarizes the data set \[54, 60, 65, 66, 67, 69, 70, 72, 73, 75, 76\], let’s first calculate the key values for the box plot.
1. **Minimum**: The smallest value in the data set is **54**.
2. **Lower Quartile (Q1)**: This is the median of the first half of the data. The first half is \[54, 60, 65, 66, 67\]. The median of this half is **65** (third value).
3. **Median (Q2)**: The overall median is the median of the entire data set. The data set is \[54, 60, 65, 66, 67, 69, 70, 72, 73, 75, 76\]. The median is the sixth value, which is **69**.
4. **Upper Quartile (Q3)**: This is the median of the second half of the data. The second half is \[69, 70, 72, 73, 75, 76\]. The median of this half is **72** (third value).
5. **Maximum**: The largest value in the data set is **76**.
Now we can summarize the findings:
- Minimum: **54**
- Q1: **65**
- Median (Q2): **69**
- Q3: **72**
- Maximum: **76**
With this information, we can construct the box plot:
- The left whisker extends from 54 to 65 (minimum to Q1).
- The box extends from 65 to 72 (Q1 to Q3).
- The line inside the box (median) is at 69.
- The right whisker extends from 72 to 76 (Q3 to maximum).
Now let's analyze the choices:
**Choice A**:
- Left whisker (54 to 67) - incorrect (Q1 should be 65)
- Box (67 to 73) - incorrect (should be 65 to 72)
- Median at 70 - incorrect (should be at 69)
- Right whisker (73 to 76) - correct
**Choice B**:
- Left whisker (54 to 65) - correct
- Box (65 to 73) - incorrect (should be 65 to 72)
- Median at 69 - incorrect (should be 69)
- Right whisker (73 to 76) - correct
**Choice C**:
- Left whisker (54 to 67) - incorrect (Q1 should be 65)
- Box (67 to 72) - incorrect (should be from 65 to 72)
- Median at 70 - incorrect (should be at 69)
- Right whisker (72 to 76) - correct
None of the provided box plots perfectly represent the calculated box plot values based on the data summary.
However, **Choice B** appears closest, featuring the correct minimum and left whisker, and having the correct overall representation of the data distribution, but with slight inaccuracies in the box section.
Thus, the best choice out of the given options would be **Choice B** despite some discrepancies.
1. **Minimum**: The smallest value in the data set is **54**.
2. **Lower Quartile (Q1)**: This is the median of the first half of the data. The first half is \[54, 60, 65, 66, 67\]. The median of this half is **65** (third value).
3. **Median (Q2)**: The overall median is the median of the entire data set. The data set is \[54, 60, 65, 66, 67, 69, 70, 72, 73, 75, 76\]. The median is the sixth value, which is **69**.
4. **Upper Quartile (Q3)**: This is the median of the second half of the data. The second half is \[69, 70, 72, 73, 75, 76\]. The median of this half is **72** (third value).
5. **Maximum**: The largest value in the data set is **76**.
Now we can summarize the findings:
- Minimum: **54**
- Q1: **65**
- Median (Q2): **69**
- Q3: **72**
- Maximum: **76**
With this information, we can construct the box plot:
- The left whisker extends from 54 to 65 (minimum to Q1).
- The box extends from 65 to 72 (Q1 to Q3).
- The line inside the box (median) is at 69.
- The right whisker extends from 72 to 76 (Q3 to maximum).
Now let's analyze the choices:
**Choice A**:
- Left whisker (54 to 67) - incorrect (Q1 should be 65)
- Box (67 to 73) - incorrect (should be 65 to 72)
- Median at 70 - incorrect (should be at 69)
- Right whisker (73 to 76) - correct
**Choice B**:
- Left whisker (54 to 65) - correct
- Box (65 to 73) - incorrect (should be 65 to 72)
- Median at 69 - incorrect (should be 69)
- Right whisker (73 to 76) - correct
**Choice C**:
- Left whisker (54 to 67) - incorrect (Q1 should be 65)
- Box (67 to 72) - incorrect (should be from 65 to 72)
- Median at 70 - incorrect (should be at 69)
- Right whisker (72 to 76) - correct
None of the provided box plots perfectly represent the calculated box plot values based on the data summary.
However, **Choice B** appears closest, featuring the correct minimum and left whisker, and having the correct overall representation of the data distribution, but with slight inaccuracies in the box section.
Thus, the best choice out of the given options would be **Choice B** despite some discrepancies.