## Dispersion, Range, standard deviation, Pharmaceutical problems

**Biostatistics and research methodology notes Unit 1**: Introduction Statistics, Biostatistics, Frequency distribution Measures of central tendency Mean, Median, Mode- Pharmaceutical examples Measures of dispersion Dispersion, Range, standard deviation, Pharmaceutical problems Correlation Definition, Karl Pearson’s coefficient of correlation, Multiple correlations – Pharmaceuticals examples

**Dispersion**

- In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a data distribution is stretched or squeezed.
- In other words, dispersion is the extent to which values in a distribution differ from the average of the distribution.
- It gives us an idea about the extent to which individual items vary from one another, and from the central value.
- It is the indication of scattering or spreading or variability of the data.
- Common examples of measures of statistical dispersion are: Range and interquartile range, Variance and Standard deviation

**Types or Classification of Measures of Dispersion**

**What are the different**

**types or classification**of Measures of DispersionAn absolute measures of dispersion

A relative measures of dispersion

**An absolute measures of dispersion**

- The measures which express the scattering of observation in terms of distances i.e., range, quartile deviation.
- The measure which expresses the variations in terms of the average of deviations of observations like mean deviation and standard deviation.

**A relative measures of dispersion**

- A relative measure of dispersion for comparing distributions of two or more data set and for unit-free comparison.
- They are the coefficient of range, the coefficient of mean deviation, the coefficient of quartile deviation, the coefficient of variation, and the coefficient of standard deviation.

**Characteristics of Measure of Dispersion**

- It have the same units as the quantity being measured.
- It shows the homogeneity or the heterogeneity of the distributionmof the observations.
- When a data set has a large value, the values in the set are widely scattered; when it is small the items in the set are tightly clustered.
- They are rigidly defined, not affected by extreme values, and not affected by sampling fluctuations.
- Measures of dispersion are type of descriptive statistics that describe how similar a set of scores are to each other.
- The more similar the scores are to each other, the lower the measure of dispersion.
- The less similar the scores are to each other, the higher the measure of dispersion.

**Example 1: Find the Standard deviation for the following set of sample data by the direct method.**

**Solution: Substitute the values in the equation and find out SD**

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