Descriptive statistics

P. MERCY RANI
M.Phil
Dept.of.education
Periyar university
Salem-11
DESCRIPTIVE STATISTICS

Measures of variability
 Measures of in variability provide formation
about the amount of spread or dispersion among
the variables.
Definitions:
 dispersion is a measure of the extent
to which the individual items vary. -
L.R connor
 dispersion is the measure of the
variation of the items.
-A.L bowley

Types of Measures of Variability
The researcher to indicate how
spread out a group of scores.
Range
Quartile Deviation
variance
standard deviation

The Range:
 The range is the difference between the largest
and smallest values in a set of values.
Range = L – S

QUARTILE DEVIATION:
It represents the difference between the third quartile
and the first quartile.
Quartile Déviation or Q.D = Q3 – Q1
2
MEAN DEVIATION:
The mean deviation is also known as the average
deviation. It is the average difference between the items
in a distribution and the median or mean of that series.
M.D. = Σ f | x |
N

Standard Deviation
The standard deviation is the square root of variance.
σ = √ Σ fx2
N
 This measure - the average of the squared
deviations from the mean is called the variance.
σ2 = Σ x2
N

MEASURES OF RELATIVE POSITIONS
 Measures of relative position indicate where is score is
in relation to all other scores in the distribution.
 Measures of relative position permit one to express
how well an individual has performed as compared to
all other individuals in the sample.
RAW SCORE
 A raw score on a test, taken by itself, has no meaning. It
gets meaning only by comparison with some reference
group or groups. The comparison may be done with
help of the following measures.

1.Sigma scores
2.Standard scores
3.Percentiles
4.Percentile ranks
Sigma scores :
 Deviation from mean expressed in (σ) terms
are called sigma scores
 The mean of a set of (σ ) scores is always and
the standard deviation is always unity
 The sigma scores are also useful in
hypothesis testing determination of
percentile ranks and probability judgments.

STANDARD SCORES OR DERIVED
SCORES
Provide information about where a score falls
in relation to the other scores in the
distribution of data
A standard score is a measure of relative
position which is appropriate when the data
represent an interval or ratio scale of
measurement. The most commonly reported
and used standard scores are T scores or Z
scores.

RAW SCORES:
 A score is numerically description of an individual’s
performance. The numerical outcome of any
evaluation done by the help of scale is called Raw
Scores.
TYPES OF SCORES:
 For the general analysis and interpretation of data
there are 4 types of standard score for the purpose of
analysis interpretation of data.
These 4 score are
1. Z score
2. z score
3. T score
4. H score

‘Z’ SCORE:
 Z score is also known as (σ) score. Z score may
be defined as basic standard score derived
from raw scores by help of its different of
mean in S.D.
“Z “SCORE:
 The standard score or Z-score involve
decimals and directional signs. To avoid this
the Z-value is multiplied by 10 and then 50 is
added. The new score is called Z-score. It is a
type of derived score where mean = 50 and
S.D = 10.
Z= 10Z +50

T SCORE:
 T score is a derived score that is 3rd type of standard
score (SS). It is a score which has been developed by
MC call. This standard score is internationally used. It
is a standard score where mean= 50, SD =10 by the
principles of conversion =
T score = 10Z+50
H SCORE:
 This score are developed by Hull. It is an important
standard score. It is a score where mean is 50 and
standard deviation is always 14. so by the principles of
conversion.
H=14Z+50

PERCENTILES:
Percentiles the points which divide the entire
scale of measurement into 100 equal parts.
They are denoted by
( p0, p1, p2,…….,p50,……,p99 ,p100 )

PERCENTILE RANKS:
 Score that divides a distribution into 100 equal parts.
 A percentile ranks indicates the percentage of scores
that fall as or below a given score (or) raw score.
 Percentile ranks help individuals interpret their test
scores in comparison to others.
 
PercentileRank
(number of data valuesbelow
0.5
the given data point)
100%
totalnumber of values
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Descriptive statistics

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Descriptive statistics