What is the standard deviation in the numbers 0, 1, 2, 3.....9, 10?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Mathematics and Logical Reasoning Problem**
**1. Question on Standard Deviation:**
What is the standard deviation in the numbers 0, 1, 2, 3, ..., 9, 10?
**2. Animal Feed Consumption Problem:**
- **Scenario 1:**
- 2 rabbits, 3 sheep, and 1 newt consume 24 lbs of feed per day.
- **Scenario 2:**
- 6 rabbits and 1 sheep consume 16 lbs of feed per day.
- **Scenario 3:**
- 2 sheep and 3 newt consume 18 lbs of food a day.
**Problem to Solve:**
How much food would 4 rabbits and 6 sheep need per day?
**Note:** The problem requires solving two parts: understanding and calculating the standard deviation for a given set of numbers and determining the feed requirement for a different combination of animals based on provided scenarios.
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Transcribed Image Text:**Educational Content: Statistical Concepts and Problem-Solving**
**Standard Deviation:**
- **Question:** What is the standard deviation in the numbers 0, 1, 2, 3, ..., 9, 10?
- **Explanation:** The standard deviation is a measure of the amount of variation or dispersion in a set of values. It indicates how much individual numbers in a dataset differ from the mean (average) of the dataset.
**Animal Feed Consumption Problem:**
- **Scenario 1:**
- 2 rabbits, 3 sheep, and 1 newt consume 24 lbs of feed per day.
- **Scenario 2:**
- 6 rabbits and 1 sheep consume 16 lbs of feed per day.
- **Scenario 3:**
- 2 sheep and 3 newt consume 18 lbs of food a day.
- **Question:** How much food would 4 rabbits and 6 sheep need per day?
**Approach:**
1. **Identify the variables:** Let R = rabbit, S = sheep, N = newt.
2. **Formulate equations based on the scenarios:**
- \(2R + 3S + 1N = 24\)
- \(6R + 1S = 16\)
- \(2S + 3N = 18\)
3. **Determine the individual consumption rates for rabbits and sheep.**
4. **Calculate the total feed needed for 4 rabbits and 6 sheep based on the rates determined.**
**Note:** This problem involves algebraic manipulation and solving systems of equations to understand how each type of animal contributes to the total feed consumption.
![### Step 1
As per our guidelines, we have to answer the first question if multiple questions are posted at a time. Please repost the rest to be answered.
### Step 2
We know that,
\[ \sigma = \sqrt{\frac{\sum (X - \mu)^2}{N}} \]
where \(\mu\) = mean of the observations.
Given: \(N = 10\)
Mean \((\mu) = \frac{1+2+3+\ldots+10}{10} = \frac{55}{10} = 5.5\)
### Step 3
\[ \Sigma (X-\mu)^2 = (1-5.5)^2 + (2-5.5)^2 + \ldots + (10-5.5)^2 \]
= 82.5
\[ \Sigma (X-\mu)^2 / N = 82.5 / 10 = 8.25 \]
Standard deviation = \(\sqrt{8.25} = \textbf{2.872281323}\).](https://content.bartleby.com/qna-images/question/20ef5b89-bdf5-4ebf-bc1c-34f412b810c9/8c9283fe-852c-4b09-8dbb-b978ae39c8ea/kloup8j_processed.jpeg)
Transcribed Image Text:### Step 1
As per our guidelines, we have to answer the first question if multiple questions are posted at a time. Please repost the rest to be answered.
### Step 2
We know that,
\[ \sigma = \sqrt{\frac{\sum (X - \mu)^2}{N}} \]
where \(\mu\) = mean of the observations.
Given: \(N = 10\)
Mean \((\mu) = \frac{1+2+3+\ldots+10}{10} = \frac{55}{10} = 5.5\)
### Step 3
\[ \Sigma (X-\mu)^2 = (1-5.5)^2 + (2-5.5)^2 + \ldots + (10-5.5)^2 \]
= 82.5
\[ \Sigma (X-\mu)^2 / N = 82.5 / 10 = 8.25 \]
Standard deviation = \(\sqrt{8.25} = \textbf{2.872281323}\).
Solution
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