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Dispersion IQV

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 wrong6 36
Wrong except self defense 11
Wrong except S.D. & rape 981
Personal choice of both parents 31961
Woman's choice25 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 fcum f
18-2217.50 22.49954 54
23-2722.50 27.49913 67
28-3227.50 32.4993 70
33-3732.50 37.4993 73
38-4237.50 42.4991 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 =

cfbelow = 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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