Chapter 4 notes

Measures of
dispersion
represent the spread or scatter of scores around
a central point or the distinguish ability of scores.
o
Expressed in terms of distance along a distribution’s horizontal,
X, axis.
o
Four measures of this are:
1) range
2) semiinterquartile range
3)standard deviation
4) index of dispersion

Measures of
SKEWNESS and
KURTOSIS represent the asymmetry and
peakednessof data.
FOUR MEASURES OF DISPERSION
1.
RangeUSED WITH MODEDISTANCE MEASUREQUANT. DATA

Simplest measure of dispersion

Distance between the largest/smallest scores.

Denoted by “R” and computed with formula:
o
R= X
u (largest score)

X
u
(smallest score)
INCLUSIVE RANGE
o
R= X
j (midpoint largest score)

X
j
(midpoint smallest score)
NONINCLUSIVE
RANGE
Often used in computer packages

the larger the range, the greater the spread or scatter of scores

not widely used!!
o
Value is determined by the two most extreme scores, so sampling stability is
very poor.*******
o
Not mathematically tractable b/c can’t be manipulated arithmetically and
algebraically.
o
Not meaningful for unordered qualitative data.
o
For QUANTITATIVE data:
Range can be reported with the mode, giving a more complete picture of
data.
However, b/c mode is often used with unordered qualitative data,
different measure of dispersion is needed.
2. SemiInterquartile RangeW/ MEDIANDISTANCE MEASUREQUANT. DATA

Based on two scores closer to the center of the distribution, so considerably more stable
than R (range).

Denoted by “Q”, is ½ the distance between the first quartile point, Q
1,
and the third quartile point, Q
3
.
o
Formula is:
Q= (Q
3
Q
1
)/ 2.
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o
Computation similar to that of the median.
(DIAGRAM BELOW
pg. 92)
o
Semiinterquartile range, Q, is half the distance from Q
1
to Q
3
.

The larger the value of Q, the greater the distance between Q
1
and Q
3
,
and the greater the spread or scatter of scores.

Often reported along with the median to give a more complete
description of data.
o
IF SYMMETRICAL, median + or  semiinterquartile range
(Mdn +/ Q)
gives
two points on X axis such that the interval between points contains 50% of scores,
but
ONLY IF ITS SYMMETRICAL!!!
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 Spring '08
 kirk
 Standard Deviation, Index of Dispersion, extreme scores, semiinterquartile range

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