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 determine the value represented by letter E on the box plot of the given data, we first need to organize the data and calculate the necessary statistics for constructing a box plot.
1. **Sort the data**: The data is already sorted:
- 45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90
2. **Find the five-number summary**:
- **Minimum (Min)**: The smallest value in the data set, which is 45.
- **First quartile (Q1)**: The median of the first half of the data (the first 6 values: 45, 45, 50, 55, 60, 65). The median of these values is the average of 50 and 55:
\[
Q1 = \frac{50 + 55}{2} = 52.5
\]
- **Median (Q2)**: The median of the entire dataset (the middle value of the 11 sorted values). The median is the 6th value (65).
- **Third quartile (Q3)**: The median of the second half of the data (the last 5 values: 65, 72, 75, 80, 80). The median of these values is the average of 72 and 75:
\[
Q3 = \frac{72 + 75}{2} = 73.5
\]
- **Maximum (Max)**: The largest value in the data set, which is 90.
3. **Summary of the five-number summary**:
- Min = 45
- Q1 = 52.5
- Median (Q2) = 65
- Q3 = 73.5
- Max = 90
4. **Box Plot**: In a box plot, typically:
- A is the minimum (45)
- B is Q1 (52.5)
- C is the median (65)
- D is Q3 (73.5)
- E is the maximum (90)
From the analysis, the value represented by the letter E in this box plot is the maximum value of the dataset, which is:
\[
\text{E} = 90
\]
Therefore, the value represented by the letter E is **90**.
1. **Sort the data**: The data is already sorted:
- 45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90
2. **Find the five-number summary**:
- **Minimum (Min)**: The smallest value in the data set, which is 45.
- **First quartile (Q1)**: The median of the first half of the data (the first 6 values: 45, 45, 50, 55, 60, 65). The median of these values is the average of 50 and 55:
\[
Q1 = \frac{50 + 55}{2} = 52.5
\]
- **Median (Q2)**: The median of the entire dataset (the middle value of the 11 sorted values). The median is the 6th value (65).
- **Third quartile (Q3)**: The median of the second half of the data (the last 5 values: 65, 72, 75, 80, 80). The median of these values is the average of 72 and 75:
\[
Q3 = \frac{72 + 75}{2} = 73.5
\]
- **Maximum (Max)**: The largest value in the data set, which is 90.
3. **Summary of the five-number summary**:
- Min = 45
- Q1 = 52.5
- Median (Q2) = 65
- Q3 = 73.5
- Max = 90
4. **Box Plot**: In a box plot, typically:
- A is the minimum (45)
- B is Q1 (52.5)
- C is the median (65)
- D is Q3 (73.5)
- E is the maximum (90)
From the analysis, the value represented by the letter E in this box plot is the maximum value of the dataset, which is:
\[
\text{E} = 90
\]
Therefore, the value represented by the letter E is **90**.