MEASURES-OF-DISPERSION.pdf

Measures of Dispersion Chapter 4: Lesson 3 1  Definition Measures of dispersion is a single value that describes the spread of a distribution. The more similar the scores are to each other, the lower the measure of dispersion will be The less simil...

Measures of Dispersion Chapter 4: Lesson 3 1  Definition Measures of dispersion is a single value that describes the spread of a distribution. The more similar the scores are to each other, the lower the measure of dispersion will be The less similar the scores are to each other, the higher the measure of dispersion will be In general, the more spread out a distribution is, the larger the measure of dispersion will be 2  Measures of Dispersion There are three main measures of dispersion: The range The interquartile range (IR) Variance / standard deviation 3  The Range The range is defined as the difference between the highest value and lowest value in the set of data, Range = HV - LV What is the range of the following data: 4 8 1 6 6 2 9 3 6 9 The highest value is 9; the lowest value is 1; the range is HV - LV = 9 - 1 = 8 4  The Interquartile Range The interquartile range (or IR) is defined as the difference of the first and third quartiles. It is the middle 50% of a set of data. The first quartile (Q1) is the 25th percentile The third quartile (Q3) is the 75th percentile IR = (Q3 - Q1) 5  Variance Variance based on the mean. This implies the squared distance of each observation from the mean: s2 is the sample variance, X is a score, X is the sample mean, and N is the number of scores 6  Standard Deviation The standard deviation is the square root of the standard variance. Take Note: Standard deviation = variance Variance = standard deviation2 7 Example Consider the following data: 28, 25, 24, 29, 33, 42, 25, 39, 32, 21, 31, 30 and 48  Range = highest value – lowest value = 48 – 21 = 27 8 Example Consider the following data: 28, 25, 24, 29, 33, 42, 25, 39, 32, 21, 31, 30 and 48 21, 24, 25, 25, 28, 29, 30, 31, 32, 33, 39, 42, 48 25% 75%  IR = (Q3 - Q1) = 36 – 25 = 11 9 x 21 31.31 10.31 106.2961 24 31.31 7.31 53.4361 25 31.31 6.31 39.8161 25 31.31 6.31 39.8161 28 31.31 3.31 10.9561 29 31.31 2.31 5.3361 30 31.31 1.31 1.7161 31 31.31 0.31 0.0961 32 31.31 0.69 0.4761 33 31.31 1.69 2.8561 39 31.31 7.69 59.1361 42 31.31 10.69 114.2761 48 31.31 16.69 278.5561 Standard deviation =7.70 N= 13 10