MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**The ages of Hampton's five cousins are listed below:**
- 15
- 20
- 5
- 13
- 16

**1) Calculate the mean (μ):**
The mean is calculated as:
\[ \mu = 14 \]

**2) Fill in the table below: Fill in the differences of each data value from the mean, then the squared differences.**

| \( x \) | \( x - \mu \) | \( (x - \mu)^2 \) |
| --- | --- | --- |
| 15 | 15 - 14 = 1 | 1^2 = 1 |
| 20 | 20 - 14 = 6 | 6^2 = 36 |
| 5  | 5 - 14 = -9 | (-9)^2 = 81 |
| 13 | 13 - 14 = -1 | (-1)^2 = 1 |
| 16 | 16 - 14 = 2 | 2^2 = 4 |

Summing the squared differences:
\[ \Sigma (x - \mu)^2 = 123 \]

**3) Calculate the population standard deviation (σ):**
The population standard deviation is calculated using the formula:
\[ \sigma = \sqrt{\frac{\Sigma (x - \mu)^2}{N}} \]

Here, \( \Sigma (x - \mu)^2 = 123 \) and \( N = 5 \).

Thus:
\[ \sigma = \sqrt{\frac{123}{5}} \approx 4.95 \]

**(Please round your answer to two decimal places.)**

This page provides a detailed guide for students learning about statistical concepts such as mean and standard deviation, with a practical example involving real data.
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Transcribed Image Text:**The ages of Hampton's five cousins are listed below:** - 15 - 20 - 5 - 13 - 16 **1) Calculate the mean (μ):** The mean is calculated as: \[ \mu = 14 \] **2) Fill in the table below: Fill in the differences of each data value from the mean, then the squared differences.** | \( x \) | \( x - \mu \) | \( (x - \mu)^2 \) | | --- | --- | --- | | 15 | 15 - 14 = 1 | 1^2 = 1 | | 20 | 20 - 14 = 6 | 6^2 = 36 | | 5 | 5 - 14 = -9 | (-9)^2 = 81 | | 13 | 13 - 14 = -1 | (-1)^2 = 1 | | 16 | 16 - 14 = 2 | 2^2 = 4 | Summing the squared differences: \[ \Sigma (x - \mu)^2 = 123 \] **3) Calculate the population standard deviation (σ):** The population standard deviation is calculated using the formula: \[ \sigma = \sqrt{\frac{\Sigma (x - \mu)^2}{N}} \] Here, \( \Sigma (x - \mu)^2 = 123 \) and \( N = 5 \). Thus: \[ \sigma = \sqrt{\frac{123}{5}} \approx 4.95 \] **(Please round your answer to two decimal places.)** This page provides a detailed guide for students learning about statistical concepts such as mean and standard deviation, with a practical example involving real data.
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