Objectives: Define measures of central tendency (mean, median, and mode) Define measures of dispersion (variance and standard deviation). Compute the measures of central tendency and Dispersion. Learn the application of mean and standard deviation using Empirical rule and Tchebyshev’s theorem. Measures of Central Tendency: A measure of the central tendency is a value about which the observations tend to cluster. In other words it is a value around which a data set is centered. The three most common measures of central tendency are mean, median and mode. A measure of the central tendency is a value about which the observations tend to cluster. In other words it is a value around which a data set is centered. The three most common measures of central tendency are mean, median and mode. A measure of the central tendency is a value about which the observations tend to cluster. In other words it is a value around which a data set is centered. The three most common measures of central tendency are mean, median and mode. A measure of the central tendency is a value about which the observations tend to cluster. In other words it is a value around which a data set is centered. The three most common measures of central tendency are mean, median and mode. Why is it needed? To summarize the data. It provides with a typical value that gives the picture of the entire data set Mean: It is the arithmetic average of a set of numbers, It is the most common measure of central tendency. Computed by summing all values in the data set and dividing the sum by the number of values in the data set Properties: Applicable for interval and ratio data Not applicable for nominal or ordinal data Affected by each value in the data set, including extreme values. Formula: Mean is calculated by adding all values in the data set and dividing the sum by the number of values in the data set. Median: Mid-point or Middle value of the data when the measurements are arranged in ascending order. A point that divides the data into two equal parts. Computational Procedure: Arrange the observations in an ascending order. If there is an odd number of terms, the median is the middle value and If there is an even number of terms, the median is the average of the middle two terms. Mode: The mode is the observation that occurs most frequently in the data set. There can be more than one mode for a data set OR there maybe no mode in a data set. Is also applicable to the nominal data. Comparison of Measures of Central Tendency in Positively Skewed Distributions: Majority of the data values fall to the left of the mean and cluster at the lower end of the distribution: the tail is to the right Mean, median & mode are different When a distribution has a few extremely high scores, the mean will have a greater value than the median = positively skewed. Majority of the data values fall to the right of the mean and cluster at the upper end of the distribution= Negatively Skewed