Question
What is the value represented by the letter E on the box plot of the data?
45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90
Enter your answer in the box.
45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90
Enter your answer in the box.
Answers
GPT-4o mini
To find the value represented by the letter E on the box plot of the given data, we first need to understand what a box plot (or box-and-whisker plot) represents.
The box plot includes the following five summary statistics of the dataset:
1. Minimum value (smallest observation)
2. First quartile (Q1 or 25th percentile)
3. Median (Q2 or 50th percentile)
4. Third quartile (Q3 or 75th percentile)
5. Maximum value (largest observation)
Let's analyze the given data:
45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90.
1. **Minimum Value**: The smallest value in the dataset is **45**.
2. **Maximum Value**: The largest value in the dataset is **90**.
3. **Median (Q2)**: To find the median, we must find the middle value of the ordered data set. Since there are 11 values (an odd number), the median will be the 6th value:
- Ordered data: 45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90.
- Median (Q2) is the 6th value: **65**.
4. **First Quartile (Q1)**: This is the median of the first half of the data (the first 6 numbers):
- First half: 45, 45, 50, 55, 60.
- Median of this subset (which is the average of the 3rd and 4th numbers, 50 and 55):
\(Q1 = \frac{50 + 55}{2} = \frac{105}{2} = 52.5\).
5. **Third Quartile (Q3)**: This is the median of the second half of the data (the last 6 numbers):
- Second half: 65, 72, 75, 80, 80, 90.
- Median of this subset (which is the average of the 3rd and 4th numbers, 75 and 80):
\(Q3 = \frac{75 + 80}{2} = \frac{155}{2} = 77.5\).
Now we have:
- Minimum = 45
- Q1 = 52.5
- Median (Q2) = 65
- Q3 = 77.5
- Maximum = 90
Assuming that "E" represents Q1 (25th percentile) on the box plot, the value is:
**E = 52.5**
Thus, entering the value: **52.5**.
The box plot includes the following five summary statistics of the dataset:
1. Minimum value (smallest observation)
2. First quartile (Q1 or 25th percentile)
3. Median (Q2 or 50th percentile)
4. Third quartile (Q3 or 75th percentile)
5. Maximum value (largest observation)
Let's analyze the given data:
45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90.
1. **Minimum Value**: The smallest value in the dataset is **45**.
2. **Maximum Value**: The largest value in the dataset is **90**.
3. **Median (Q2)**: To find the median, we must find the middle value of the ordered data set. Since there are 11 values (an odd number), the median will be the 6th value:
- Ordered data: 45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90.
- Median (Q2) is the 6th value: **65**.
4. **First Quartile (Q1)**: This is the median of the first half of the data (the first 6 numbers):
- First half: 45, 45, 50, 55, 60.
- Median of this subset (which is the average of the 3rd and 4th numbers, 50 and 55):
\(Q1 = \frac{50 + 55}{2} = \frac{105}{2} = 52.5\).
5. **Third Quartile (Q3)**: This is the median of the second half of the data (the last 6 numbers):
- Second half: 65, 72, 75, 80, 80, 90.
- Median of this subset (which is the average of the 3rd and 4th numbers, 75 and 80):
\(Q3 = \frac{75 + 80}{2} = \frac{155}{2} = 77.5\).
Now we have:
- Minimum = 45
- Q1 = 52.5
- Median (Q2) = 65
- Q3 = 77.5
- Maximum = 90
Assuming that "E" represents Q1 (25th percentile) on the box plot, the value is:
**E = 52.5**
Thus, entering the value: **52.5**.