Question:
The measurement of dispersion or spread of data points around their mean value is called
The measurement of dispersion or spread of data points around their mean value is called
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To distinguish between Range and Standard Deviation: Range tells you the total distance between the absolute outer boundaries of your data. Standard Deviation shows the average "distance from the center" for all data points combined.
Updated On: Jun 23, 2026
- Coefficient of determination
- Mode
- Range
- Standard Deviation
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The Correct Option is D
Solution and Explanation
Concept:
In statistics, descriptive metrics are divided into measures of central tendency (which find the center of the data) and measures of dispersion (which describe how scattered or spread out the data points are around that center).
Step 1: Analyzing the technical definition of Standard Deviation.
The standard deviation ($\sigma$ for a population, $s$ for a sample) measures the average distance of each data point from the statistical mean ($\mu$) of the dataset. It is mathematically formulated as the square root of the variance: $$ \sigma = \sqrt{\frac{\sum_{i=1}^{n} (X_i - \mu)^2}{n}} $$ Because it squares the differences before averaging them, it accounts for how every single data point deviates from the mean. It uses the same units as the original data, making it the most reliable tool for evaluating data variability in engineering and planning.
Step 2: Evaluating why the other options do not fit this specific definition.
• Coefficient of Determination ($R^2$): A metric used in regression analysis to show the proportion of variance in a dependent variable that is predictable from an independent variable. It is not a direct measure of data dispersion.
• Mode: The value that appears most frequently in a dataset. This is a measure of central tendency, not dispersion.
• Range: The difference between the highest and lowest values ($X_{\text{max}} - X_{\text{min}}$). While it does show dispersion, it only looks at the two extreme values and ignores how the rest of the data points spread around the mean. Therefore, standard deviation is the correct measurement of data spread around the mean value.
Step 1: Analyzing the technical definition of Standard Deviation.
The standard deviation ($\sigma$ for a population, $s$ for a sample) measures the average distance of each data point from the statistical mean ($\mu$) of the dataset. It is mathematically formulated as the square root of the variance: $$ \sigma = \sqrt{\frac{\sum_{i=1}^{n} (X_i - \mu)^2}{n}} $$ Because it squares the differences before averaging them, it accounts for how every single data point deviates from the mean. It uses the same units as the original data, making it the most reliable tool for evaluating data variability in engineering and planning.
Step 2: Evaluating why the other options do not fit this specific definition.
• Coefficient of Determination ($R^2$): A metric used in regression analysis to show the proportion of variance in a dependent variable that is predictable from an independent variable. It is not a direct measure of data dispersion.
• Mode: The value that appears most frequently in a dataset. This is a measure of central tendency, not dispersion.
• Range: The difference between the highest and lowest values ($X_{\text{max}} - X_{\text{min}}$). While it does show dispersion, it only looks at the two extreme values and ignores how the rest of the data points spread around the mean. Therefore, standard deviation is the correct measurement of data spread around the mean value.
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