Statistics -Descriptive statistics 2013/09/30

Descriptive statistics Numerical measures of location, dispersion, shape, and association are also used to summarized data. A population is the set of all elements of interest in a particular study. A sample is a subset of the population. If the measures are computed from a population, they are called population parameters. If the measures are computed from a sample, they are called sample statistics.

Measures of location Mean – Sample mean – Population mean – P84. Table 3.1

Measures of location Median – Arrange the data in ascending order the median is the middle value (for odd number) or the average of the two middle values (for even number) Mode – The mode is the value that occurs with greatest frequency.

Measures of location Percentile – The pth percentile is a value such that at least p percent of the observations are less than or equal to this value and at least (100-p) percent of the observations are greater than or equal to this value. Quartile – It is desirable to divide data into four parts: Q1 (=25 th percentile), Q2 (= 50 th percentile), Q3 (=75 th percentile)

Measures of variability Range – Largest value – smallest value Interquartile range – IQR = Q3 – Q1

Measures of variability Variance – Sample variance – Population variance – P94. Table 3.4

Measures of variability Standard deviation – Sample standard deviation – Population standard deviation Coefficient of variation – For a sample – For a population

Measures of association between two variables Covariance – Sample covariance – Population covariance Correlation coefficient – Sample – Population