Measures of Dispersion Importance of Dispersion Types of

Measures of Dispersion Importance of Dispersion Types of measures of Dispersion Range Interquartile range Variance and Standard deviation

Importance of Dispersion In some cases, two sets of data with same mean and same median, but don’t mean that they have the same dispersion. E. g. X : 80, 90, 100, 110, 120 Y : 0, 50, 100, 150, 200 Mean of X = Mean of Y = Median of X and median of Y = 100 But Y is more dispersed than X.

Types of measure of dispersion There are three types of measure of dispersion: - Range - Interquartile range - Variance and Standard deviation

Range What is range? Ans: The highest score in a distribution minus the lowest score. Example: There are two sets of data about the amount of rainfall (mm) in Taipei and Hong Kong. Range of Taipei = (305 - 66)mm = 239 mm Range of Seoul = (252 -13)mm = 239 mm Therefore they have the same range.

Interquartile range What is interquartile range? Ans: The difference between the upper and the lower quartiles: IQR = 3 rd quartile - 1 st quartile Example:

From the graph, the upper quartile = the 150 th value = 177 cm the lower quartile = the 50 th value = 168 cm therefore, the interquartile range = the upper quartile - lower quartile = 177 cm - 168 cm = 9 cm

Variance and Standard deviation What is variance? Ans: The mean of the squared deviation scores about the mean of a distribution. What is standard deviation? Ans: The square root of the mean of the squared deviation scores about the mean of a distribution; more simply, the square root of the variance. Example: The following are two sets of data of an experiment obtained by two different students.

1). What is the mean volume of acid measured by each student? Ans: Mean of student A = = 9. 8 Mean of student B = = 10

2). What is the standard deviation? Ans: Standard deviation of X: = = 3. 0265 Standard deviation of Y: = = 2. 757 3). Which set of results is more reliable? Ans: Y

Conclusion The range and interquartile range are usually ineffective to measure the dispersion of a set of data. An useful measure that describes the dispersion of all the values is the variance or standard deviation.

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