The distribution below is… Perfectly normally distributed
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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The distribution below is…
Perfectly normally distributed
Positively skewed, thus skewed to the right.
Positively skewed, thus skewed to the left.
Negatively skewed, thus skewed to the left.

Transcribed Image Text:The graph displayed is a density plot, which is commonly used in statistics to estimate the probability distribution of a continuous variable. Here, the horizontal axis (X-axis) is labeled "Score," representing the different values that the continuous variable can take. The vertical axis (Y-axis) is labeled "Density," which signifies the probability density of the scores.
**Explanation of the Graph:**
1. **Shape of the Curve**: The curve rises from the left, peaks, and then falls off towards the right. This shape indicates the distribution of scores.
2. **Peak (Mode)**: The highest point of the curve represents the score with the highest density, i.e., the score that occurs most frequently within the dataset.
3. **Skewness**: The curve is not symmetrical, indicating that the distribution of scores is skewed. The left side rises more steeply, and the right side descends more gradually. This indicates a right-skewed distribution, where the bulk of the scores fall towards the lower end of the scale, while fewer scores extend towards the higher end.
4. **Density Interpretation**: The area under the curve represents the probability distribution. The total area under the curve sums up to 1, which is a characteristic of all probability density functions.
**Usage in Education**:
Density plots are useful in educational settings for visualizing the distribution of test scores, grades, or any other continuous data. They help educators identify patterns such as:
- Where most students' scores lie.
- The variability in scores.
- Presence of outliers or unusually high/low scores.
Understanding these patterns can guide instructional improvements and highlight areas where students may require additional support.
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