2. The test scores, of 16 students are listed below: 44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97. (b) Find the first quartile of the above data,
2. The test scores, of 16 students are listed below: 44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97. (b) Find the first quartile of the above data,
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Analyzing Test Scores of Students
**Problem Statement:**
2. The test scores of 16 students are listed below:
44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97.
(b) Find the first quartile of the above data.
**Options:**
- ⃝ 87
- ⃝ 88.5
- ⃝ 58.5
- ⃝ 57
**Explanation:**
To find the first quartile (Q1) of a data set, which is the median of the lower half of the data, follow these steps:
1. Arrange the data in ascending order (already provided in the problem):
44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97.
2. Since there are 16 data points (an even number), the lower half consists of the first 8 numbers (first eight values):
44, 46, 51, 57, 60, 63, 65, 70.
3. Find the median of these first 8 numbers:
- The median is the average of the 4th and 5th numbers when arranged in ascending order.
- The 4th number is 57 and the 5th number is 60.
4. Calculate the median (First Quartile):
\[
Q1 = \frac{57 + 60}{2} = 58.5
\]
Therefore, the first quartile (Q1) of the given data is **58.5**.
The correct option is:
- ⃝ **58.5**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae25ab45-ae90-481a-a08d-38576354b5ac%2Fee2bb06a-4547-4eda-9a52-f2d95f95e913%2Ffcrcp4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analyzing Test Scores of Students
**Problem Statement:**
2. The test scores of 16 students are listed below:
44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97.
(b) Find the first quartile of the above data.
**Options:**
- ⃝ 87
- ⃝ 88.5
- ⃝ 58.5
- ⃝ 57
**Explanation:**
To find the first quartile (Q1) of a data set, which is the median of the lower half of the data, follow these steps:
1. Arrange the data in ascending order (already provided in the problem):
44, 46, 51, 57, 60, 63, 65, 70, 75, 76, 85, 87, 90, 94, 95, 97.
2. Since there are 16 data points (an even number), the lower half consists of the first 8 numbers (first eight values):
44, 46, 51, 57, 60, 63, 65, 70.
3. Find the median of these first 8 numbers:
- The median is the average of the 4th and 5th numbers when arranged in ascending order.
- The 4th number is 57 and the 5th number is 60.
4. Calculate the median (First Quartile):
\[
Q1 = \frac{57 + 60}{2} = 58.5
\]
Therefore, the first quartile (Q1) of the given data is **58.5**.
The correct option is:
- ⃝ **58.5**
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