Dispersion of data is measured by -a) Coefficient of correlationb) Rangec) Standard deviationd) Coefficient of variatione) Normal distribution curve
## Core Concept
Dispersion of data, also known as variability or spread, refers to the extent to which data points in a dataset deviate from the central tendency (mean, median, or mode). Measures of dispersion provide a quantitative measure of the variability in a dataset.
## Why the Correct Answer is Right
The correct answer involves identifying which of the options are indeed measures of dispersion.
- **Range (b)**: This is the simplest measure of dispersion, calculated as the difference between the highest and lowest values in a dataset.
- **Standard deviation (c)**: This measures the average distance of individual data points from the mean value. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.
- **Coefficient of variation (d)**: This is a relative measure of dispersion, expressed as a percentage. It is the ratio of the standard deviation to the mean, multiplied by 100. It is used to compare the variability of datasets with different units or scales.
## Why Each Wrong Option is Incorrect
- **Option A: Coefficient of correlation (a)**: This measures the strength and direction of a linear relationship between two variables on a scatterplot. It does not measure dispersion.
- **Option E: Normal distribution curve (e)**: While a normal distribution curve can provide insights into the dispersion of data (through its standard deviation), the curve itself is not a measure of dispersion but rather a graphical representation of how data points are distributed.
## Clinical Pearl / High-Yield Fact
A key point to remember is that when comparing variability across different datasets, especially those with different units or scales, the **coefficient of variation** is particularly useful because it standardizes the dispersion by the mean, allowing for more direct comparisons.
## Correct Answer: C.