Chapter 5 Measures of Variability Example For Students

Chapter 5: Measures of Variability Question Answer What is the Measure of variability? It is a number that describes diversity or variability in the distribution. Basically it shows us how much variation and diversity there is within the answers we received. What are the five measures of variability? The index of qualitative variation, The range, The interquartile rage, The standard deviation and The variance What is the Index of Qualitative Variation (IQV)? It is a measure of variability for nominal variables like race or ethnicity. What is the range of the Index of Qualitative Variation (IQV)? It is a number that can range from 0.00 to 1.00. What is the value of the IQV if there is no variation? 0.00 What is the value of the IQV if there is maximum variation? 1.00 What is the equation for calculating the IQV? IQV = Total Observed Differences / Total Possible Differences OR IQV = K(n2 – ?f2) / n2 (K-1) What is the IQV based on? it is based on a ratio of the total number of differences in the distribution to the maximum number of possible differences within the same distribution. What is the range? it is the difference between the highest score and lowest score in the distribution. Which level of variables does the range measure? The Ordinal level What is the Inter-Quartile Range (IQR)? The width of the middle 50 percent of the distribution. It is defined as the difference between the lower and upper quartiles (Q1 and Q3.) What is the equation for the IQR? IQR= Q3-Q1 How is the Box Plot used? It is a graphic device that visually presents the following elements: the range, the inter-quartile range, the median, the quartiles, the minimum (lowest value,) and the maximum (highest value.) How do you calculate the first quartile (q1)? Q1= n (.25) How do you calculate the third quartile (q3)? Q3= n (.75) Where do you start when you are identifying the values associated with the first and third quartile? The bottom, or smallest value (assuming the values are already ordered from highest to lowest) What is the variance? It is the average of the squared deviations for the mean of the distribution. What is the standard deviation? It is the square root of the variance Which measures of variability measure Interval-Ratio variables? Variance and Standard Deviation. What is the equation for finding the variation? sy2= E (Y-Y)^2 / N-1