1) (15 Points) Find the mode, median and mean of the data set below. Then, use the computational formula to find the standard deviation s. {12, 11, 15, 12, 20} Mode: 12 121 12 12 12 15 Median: 144 144 225 14 Mean: 2D 400 Standard dev.: Ex= 70 Ex21034 ftho pumher Y
1) (15 Points) Find the mode, median and mean of the data set below. Then, use the computational formula to find the standard deviation s. {12, 11, 15, 12, 20} Mode: 12 121 12 12 12 15 Median: 144 144 225 14 Mean: 2D 400 Standard dev.: Ex= 70 Ex21034 ftho pumher Y
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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![**Problem Statement:**
1) (15 Points) Find the mode, median, and mean of the data set below. Then, use the computational formula to find the standard deviation \( s \).
Data set: \{12, 11, 15, 12, 20\}
**Solutions:**
- **Mode:** 12
- **Median:** 12
- **Mean:** 14
- **Standard Deviation:** __________
**Data Analysis Table:**
| \( x \) | \( x^2 \) |
|---------|-----------|
| 11 | 121 |
| 12 | 144 |
| 12 | 144 |
| 15 | 225 |
| 20 | 400 |
- \(\Sigma x = 70\)
- \(\Sigma x^2 = 1034\)
**Explanation:**
- **Mode:** The mode is the most frequently occurring number in the data set, which is 12.
- **Median:** The median is the middle number when the data set is ordered. When arranged (11, 12, 12, 15, 20), the median is 12.
- **Mean:** The mean is the average of the numbers, calculated by dividing the sum of the numbers by the number of observations. Here, it is calculated as \( \frac{70}{5} = 14 \).
- **Standard Deviation:** Not calculated in the image. Use the standard deviation formula for calculation:
\[ s = \sqrt{\frac{\Sigma x^2 - \frac{(\Sigma x)^2}{n}}{n-1}} \]
where \( n = 5 \), \(\Sigma x = 70\), \(\Sigma x^2 = 1034\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90255ae0-b96f-4088-a274-ba70795c82ba%2F5f370ee1-9d10-4de2-8efa-55bbd16c0601%2Fdjv9w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
1) (15 Points) Find the mode, median, and mean of the data set below. Then, use the computational formula to find the standard deviation \( s \).
Data set: \{12, 11, 15, 12, 20\}
**Solutions:**
- **Mode:** 12
- **Median:** 12
- **Mean:** 14
- **Standard Deviation:** __________
**Data Analysis Table:**
| \( x \) | \( x^2 \) |
|---------|-----------|
| 11 | 121 |
| 12 | 144 |
| 12 | 144 |
| 15 | 225 |
| 20 | 400 |
- \(\Sigma x = 70\)
- \(\Sigma x^2 = 1034\)
**Explanation:**
- **Mode:** The mode is the most frequently occurring number in the data set, which is 12.
- **Median:** The median is the middle number when the data set is ordered. When arranged (11, 12, 12, 15, 20), the median is 12.
- **Mean:** The mean is the average of the numbers, calculated by dividing the sum of the numbers by the number of observations. Here, it is calculated as \( \frac{70}{5} = 14 \).
- **Standard Deviation:** Not calculated in the image. Use the standard deviation formula for calculation:
\[ s = \sqrt{\frac{\Sigma x^2 - \frac{(\Sigma x)^2}{n}}{n-1}} \]
where \( n = 5 \), \(\Sigma x = 70\), \(\Sigma x^2 = 1034\).
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