INDEX OF QUALITATIVE VARIATION: (for Nominal and discrete Ordinal Data)

IQV measures the ratio of the actual variation divided by the highest possible variation

IQV=

where: k = # of categories

N = # of cases

f² = sum of the squared frequencies

Example:

ABORTIONS	f	f2
Always wrong	6	36
Wrong except self defense	1	1
Wrong except S.D. & rape	9	81
Personal choice of both parents	31	961
Woman's choice	25	625
N =	75	1,704

Q: What is spread or variation in abortion attitudes?

A: IQV =

SOURCE: STUDENT SURVEY SDSU 1995

Interpretation:

B. Interval Data and continuous Ordinal Data: Range

Range is found by subtracting the lower true limit of the lowest category from the upper true limit of the highest category.

Example: Ages of Sociology 201 Students

Ages (NB)	lower true limit	upper true limit	f	cum f
18-22	17.50	22.499	54	54
23-27	22.50	27.499	13	67
28-32	27.50	32.499	3	70
33-37	32.50	37.499	3	73
38-42	37.50	42.499	1	74
			74 = N

SOURCE: STUDENT SURVEY SDSU 1995

Example: 42.499 - 17.50 = 25 The range of this sample is 25 years.

C. Inter Quartile Range: measure the range of the middle 50% .

IQR = P₇₅ - P₂₅ where: (note the 75 to 25 could be any range but this specifies the middle 50%)

P₇₅ = P₂₅ =

cf_below = cumulative frequency below interval containing the percentile.

f = the number of cases in the interval containing the percentile.

i = width of interval

N = total number in sample

LTL = lower true limit of the interval containing the percentile.

P₇₅ = P₂₅ =

23.077 - 17.519 = 5.56 years

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