Question 1175771: Examine the three sample of data shown below. Without performing any calculation, indicate which sample has the largest amount of variability and which sample has the least amount of variability. Explain why,
1. 27,39,22,36,31
2. 32,28,33,30,27
3. 34,47,16,49,39
Calculate Mean deviation for median and variance of the above three samples. And discuss which one indicate which sample has the least amount of variability and why?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Absolutely, let's analyze the variability of these samples.
**Initial Assessment (Without Calculation)**
* **Largest Variability:** Sample 3 (34, 47, 16, 49, 39)
* This sample has the widest range of values. The difference between the smallest (16) and largest (49) values is substantial, suggesting high variability.
* **Least Variability:** Sample 2 (32, 28, 33, 30, 27)
* The values in this sample are clustered relatively close together. The range is much smaller than in the other samples, indicating low variability.
**Calculations and Detailed Analysis**
Using the provided python code, and its output, here is the result of the calculations.
* **Sample 1:**
* Mean Deviation: 5.2
* Variance: 37.2
* **Sample 2:**
* Mean Deviation: 2.0
* Variance: 5.2
* **Sample 3:**
* Mean Deviation: 9.2
* Variance: 139.6
**Discussion**
* **Sample 2 (Least Variability):**
* The calculations confirm our initial observation. Sample 2 has the lowest mean deviation (2.0) and the lowest variance (5.2). This means that, on average, the values in this sample deviate the least from their median and mean. The data points are tightly clustered around the central tendency.
* **Sample 3 (Largest Variability):**
* Sample 3 has the highest mean deviation (9.2) and the highest variance (139.6). This confirms its high variability. The values are spread out over a much wider range, leading to greater deviations from the central tendency.
**Why These Metrics Indicate Variability**
* **Mean Deviation from the Median:**
* This metric measures the average absolute difference between each data point and the median. A lower mean deviation indicates that the data points are closer to the median, implying less variability.
* **Variance:**
* Variance measures the average squared deviation of each data point from the mean. A lower variance indicates that the data points are closer to the mean, implying less spread and therefore less variability.
In conclusion, Sample 2 exhibits the least variability because its data points are most closely clustered around the central tendency, while Sample 3 exhibits the most variability due to its widely dispersed data points.
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