For each of 25 students in a class, a teaching assistant is noting down the marks obtained by the students in the midterm (out of 50). The data are: 11, 47, 18, 42, 34, 13, 11, 37, 23, 46, 13, 19, 48, 16, 31, 39, 48, 43, 50, 10, 10, 49, 37, 25, 29. HINT: The sum of the values: 749 Ordered data: 10, 10, 11, 11, 13, 13, 16, 18, 19, 23, 25, 29, 31, 34, 37, 37, 39, 42, 43, 46, 47, 48, 48, 49, 50. a) Determine the mean, median, the quartiles (Q1 and Q3), and the IQR. Are there outliers? b) Construct the modified boxplot for this data.
For each of 25 students in a class, a teaching assistant is noting down the marks obtained by the students in the midterm (out of 50). The data are: 11, 47, 18, 42, 34, 13, 11, 37, 23, 46, 13, 19, 48, 16, 31, 39, 48, 43, 50, 10, 10, 49, 37, 25, 29. HINT: The sum of the values: 749 Ordered data: 10, 10, 11, 11, 13, 13, 16, 18, 19, 23, 25, 29, 31, 34, 37, 37, 39, 42, 43, 46, 47, 48, 48, 49, 50. a) Determine the mean, median, the quartiles (Q1 and Q3), and the IQR. Are there outliers? b) Construct the modified boxplot for this data.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![### Statistical Analysis of Student Midterm Scores
For each of 25 students in a class, a teaching assistant is noting down the marks obtained by the students in the midterm (out of 50). The data are:
11, 47, 18, 42, 34, 13, 11, 37, 23, 46, 13, 19, 48, 16, 31, 39, 48, 43, 50, 10, 10, 49, 37, 25, 29.
**HINT:**
- The sum of the values: 749
- Ordered data: 10, 10, 11, 11, 13, 13, 16, 18, 19, 23, 25, 29, 31, 34, 37, 37, 39, 42, 43, 46, 47, 48, 48, 49, 50.
**Tasks:**
a) Determine the mean, median, the quartiles (Q1 and Q3), and the IQR. Identify any potential outliers.
b) Construct the modified boxplot for this data.
---
### Analysis:
#### a) Determining Statistical Measures:
1. **Mean:**
\[
\text{Mean} = \frac{\text{Sum of the values}}{\text{Number of values}} = \frac{749}{25} = 29.96
\]
2. **Median:**
- The median is the middle value in an ordered dataset.
- For 25 values, the median is the 13th value in the ordered list:
\[
\text{Median} = 29
\]
3. **Quartiles:**
- **First Quartile (Q1):** The median of the first half of the ordered dataset (values 1 to 12):
\[
Q1 = 13
\]
- **Third Quartile (Q3):** The median of the second half of the ordered dataset (values 14 to 25):
\[
Q3 = 43
\]
4. **Interquartile Range (IQR):**
\[
\text{IQR} = Q3 - Q1 = 43 - 13 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb1f1461-965e-4f7c-b232-2dc7e5366365%2F24adb34f-6a7e-45d7-b82c-9d89aab9e934%2F2uuz7fn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Student Midterm Scores
For each of 25 students in a class, a teaching assistant is noting down the marks obtained by the students in the midterm (out of 50). The data are:
11, 47, 18, 42, 34, 13, 11, 37, 23, 46, 13, 19, 48, 16, 31, 39, 48, 43, 50, 10, 10, 49, 37, 25, 29.
**HINT:**
- The sum of the values: 749
- Ordered data: 10, 10, 11, 11, 13, 13, 16, 18, 19, 23, 25, 29, 31, 34, 37, 37, 39, 42, 43, 46, 47, 48, 48, 49, 50.
**Tasks:**
a) Determine the mean, median, the quartiles (Q1 and Q3), and the IQR. Identify any potential outliers.
b) Construct the modified boxplot for this data.
---
### Analysis:
#### a) Determining Statistical Measures:
1. **Mean:**
\[
\text{Mean} = \frac{\text{Sum of the values}}{\text{Number of values}} = \frac{749}{25} = 29.96
\]
2. **Median:**
- The median is the middle value in an ordered dataset.
- For 25 values, the median is the 13th value in the ordered list:
\[
\text{Median} = 29
\]
3. **Quartiles:**
- **First Quartile (Q1):** The median of the first half of the ordered dataset (values 1 to 12):
\[
Q1 = 13
\]
- **Third Quartile (Q3):** The median of the second half of the ordered dataset (values 14 to 25):
\[
Q3 = 43
\]
4. **Interquartile Range (IQR):**
\[
\text{IQR} = Q3 - Q1 = 43 - 13 =
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