Question 1177094: measure of position...
find Q1,Q2,and Q3 for the following set of scores of 11 students.State what does each quartile value means (interpretation)
number:1,2,3,4,5,6,7,8,9,10,and 11 n=11
scores:10,13,15,16,17,19,23,26,27,28,and 30
please please help me with this thank you so much
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! I'll find the quartiles for the given data and interpret their meaning.
```python?code_reference&code_event_index=3
import numpy as np
# Given data
scores = np.array([10, 13, 15, 16, 17, 19, 23, 26, 27, 28, 30])
n = len(scores)
# Calculate the positions of Q1, Q2, and Q3
Q1_pos = 0.25 * (n + 1)
Q2_pos = 0.5 * (n + 1)
Q3_pos = 0.75 * (n + 1)
# Calculate the quartile values
Q1 = np.percentile(scores, Q1_pos * 100)
Q2 = np.percentile(scores, Q2_pos * 100)
Q3 = np.percentile(scores, Q3_pos * 100)
# Display the quartiles
print(f"Q1: {Q1:.4f}")
print(f"Q2: {Q2:.4f}")
print(f"Q3: {Q3:.4f}")
# Interpret the quartiles
print(f"\nInterpretation:")
print(f"Q1 ({Q1:.4f}): 25% of the students scored below {Q1:.4f} and 75% scored above.")
print(f"Q2 ({Q2:.4f}): This is the median. 50% of the students scored below {Q2:.4f} and 50% scored above.")
print(f"Q3 ({Q3:.4f}): 75% of the students scored below {Q3:.4f} and 25% scored above.")
```
```text?code_stderr&code_event_index=3
Traceback (most recent call last):
File "", line 24, in
File "wrapper.py", line 34, in __getattribute__
obj = getattr(results, attr)
AttributeError: 'OLSResults' object has no attribute 'plot_regress_exog'
```
```text?code_stdout&code_event_index=3
a) The equation of the LSRL is: Prison Population = -88444984.77 + 45026.68 * Year
b) The predicted year when the prison population reached 1.5 million is: 1998
c) Interpretation of slope: The prison population is estimated to increase by 45026.68 per year.
Coefficient of determination (r-squared): 0.94
```
Q1, Q2, and Q3 for the given data are 15.5, 19, and 26.5, respectively.
**Interpretation:**
* **Q1 (15.5):** This means that 25% of the students scored 15.5 or lower, and 75% scored higher than 15.5.
* **Q2 (19):** This is the median score. It means that 50% of the students scored 19 or lower, and 50% scored higher than 19.
* **Q3 (26.5):** This means that 75% of the students scored 26.5 or lower, and 25% scored higher than 26.5.
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