Consider the following two variables: Frequency 0 2 4 6 8 10 Variable 1 Frequency 02 4 6 8 10 0 2 4 6 8 10 (a) Which variable has the higher standard deviation? O Variable 2 O Variable 1 O They have the same standard deviation 0 2 Variable 2 4 6 8 10 (b) Suppose a new data point at 0 was added in both of the datasets. What would happen to the standard deviations? The standard deviation for Variable 1 would not change The standard deviation for Variable 2 would not change
Consider the following two variables: Frequency 0 2 4 6 8 10 Variable 1 Frequency 02 4 6 8 10 0 2 4 6 8 10 (a) Which variable has the higher standard deviation? O Variable 2 O Variable 1 O They have the same standard deviation 0 2 Variable 2 4 6 8 10 (b) Suppose a new data point at 0 was added in both of the datasets. What would happen to the standard deviations? The standard deviation for Variable 1 would not change The standard deviation for Variable 2 would not change
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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- Data is represented by a bar histogram.
- X-axis: Represents the data points ranging from 0 to 10.
- Y-axis: Represents the frequency of each data point.
- The distribution appears to be bimodal with peaks around values 2 and 8.
#### Variable 2
- Data is represented by a bar histogram.
- X-axis: Represents the data points ranging from 0 to 10.
- Y-axis: Represents the frequency of each data point.
- The distribution appears to be unimodal, centered around the value of 5.
### Questions for Analysis
**(a) Which variable has the higher standard deviation?**
- **Variable 2**
- **Variable 1** ⬤
- **They have the same standard deviation**
*Hint: Standard deviation measures how spread out the data points are around the mean. More spread implies a higher standard deviation.*
**(b) Suppose a new data point at 0 was added to both datasets. What would happen to the standard deviations?**
- The standard deviation for Variable 1 would ⬤ **not change**.
- The standard deviation for Variable 2 would ⬤ **not change**.
*Hint: Adding a data point at 0 to both datasets would either increase the spread, decrease it, or have no impact on standard deviation.*
*Note: The above options indicate the analyses selected by the student.*
### Detailed Graph Explanation
**Graph for Variable 1:**
- The histogram for Variable 1 showcases a bimodal distribution, where two peaks are visible. The bars for values around 2 and 8 are higher, indicating these data points have the highest frequencies.
**Graph for Variable 2:**
- The histogram for Variable 2 showcases a unimodal distribution, centered around the value 5. Most data points are concentrated around this central value, forming a symmetric shape typically indicative of a normal distribution.
### Conclusion
Interpreting histograms and understanding standard deviation is crucial in statistics. Variable 1 likely has a higher standard deviation due to its bimodal nature and wider spread of data points, whereas Variable 2 has a more concentrated spread around its central value. Adding a new data point at 0 would not](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F786a2b18-36fc-4a59-90dc-399df5403cec%2F6c29e534-356b-4c27-a579-664a6540bf62%2Fid9oas_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Standard Deviation with Histogram Examples
Consider the following two variables illustrated in the histograms below:
#### Variable 1
- Data is represented by a bar histogram.
- X-axis: Represents the data points ranging from 0 to 10.
- Y-axis: Represents the frequency of each data point.
- The distribution appears to be bimodal with peaks around values 2 and 8.
#### Variable 2
- Data is represented by a bar histogram.
- X-axis: Represents the data points ranging from 0 to 10.
- Y-axis: Represents the frequency of each data point.
- The distribution appears to be unimodal, centered around the value of 5.
### Questions for Analysis
**(a) Which variable has the higher standard deviation?**
- **Variable 2**
- **Variable 1** ⬤
- **They have the same standard deviation**
*Hint: Standard deviation measures how spread out the data points are around the mean. More spread implies a higher standard deviation.*
**(b) Suppose a new data point at 0 was added to both datasets. What would happen to the standard deviations?**
- The standard deviation for Variable 1 would ⬤ **not change**.
- The standard deviation for Variable 2 would ⬤ **not change**.
*Hint: Adding a data point at 0 to both datasets would either increase the spread, decrease it, or have no impact on standard deviation.*
*Note: The above options indicate the analyses selected by the student.*
### Detailed Graph Explanation
**Graph for Variable 1:**
- The histogram for Variable 1 showcases a bimodal distribution, where two peaks are visible. The bars for values around 2 and 8 are higher, indicating these data points have the highest frequencies.
**Graph for Variable 2:**
- The histogram for Variable 2 showcases a unimodal distribution, centered around the value 5. Most data points are concentrated around this central value, forming a symmetric shape typically indicative of a normal distribution.
### Conclusion
Interpreting histograms and understanding standard deviation is crucial in statistics. Variable 1 likely has a higher standard deviation due to its bimodal nature and wider spread of data points, whereas Variable 2 has a more concentrated spread around its central value. Adding a new data point at 0 would not
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