Question

1. What are measures of variability? What do they measure? 5. Below are two groups of prisoners, classified according to booking offense. Find the index of qualitative variation (IQV) for each group (

Answer 1

The Index of Qualitative Variation (IQV) for Group 1 is 0.67, and for Group 2, it is 0.50.

Step-by-step explanation:

Measures of variability, such as the Index of Qualitative Variation (IQV), assess the diversity or spread of values within a dataset. IQV specifically quantifies the diversity in the distribution of a categorical variable. To calculate IQV, you use the formula:

`\[IQV = (1)/(K-1) \sum_(i=1)^(K) p_i(1-p_i)\]`

Where K is the number of categories, and
`\(p_i\)` is the proportion of cases in category i.

For Group 1:

`\[IQV_(Group 1) = (1)/(4-1) [(0.5)(1-0.5) + (0.25)(1-0.25) + (0.25)(1-0.25)] = 0.67\]`

For Group 2:

`\[IQV_(Group 2) = (1)/(4-1) [(0.2)(1-0.2) + (0.2)(1-0.2) + (0.4)(1-0.4) + (0.2)(1-0.2)] = 0.50\]`

In Group 1, the IQV of 0.67 indicates a higher diversity in booking offenses compared to Group 2, which has an IQV of 0.50. This means that, on average, there is greater variability in the types of offenses in Group 1. The IQV values help quantify and compare the heterogeneity or variability in the distribution of qualitative data between the two groups.

Full Question:

1. What are measures of variability? What do they measure? 5. Below are two groups of prisoners, classified according to booking offense. Find the index of qualitative variation (IQV) for each group(see Table 4.1).

Trait Group 1 Group2

Robbery 50 20

Burglary 30 10

Larceny 70 60

Auto Theft 0 30