QUESTION
Explain different measures of dispersion used in educational research.
- Course: Educational Statistics
- Course code 8614
- Level: B.Ed Solved Assignment
ANSWER
Introduction to Measures of Dispersion
Measures of central tendency
focus on what is an average or in the middle of the distribution of scores.
Often the information provided by these measures does not give us a clear picture
of the data and we need something more. It means that knowing the mean, median,
and mode of a distribution does allow us to differentiate between two or more than
two distributions; and we need additional information about the distribution.
This additional information is provided by a series of measures which are
commonly known as measures of dispersion.
There is dispersion when there is
dissimilarity among the data values. The greater the dissimilarity, the greater
the degree of dispersion will be.
Measures of dispersion are needed
for four basic purposes.
i) To determine the reliability of an average.
ii) To serve as a basis for the control of the
variability.
iii) To compare two or more series about
their variability.
iv) To facilitate the use of other statistical
measures.
The measure of dispersion enables us
to compare two or more series concerning their variability. It is also
looked at as a means of determining uniformity or consistency. A high degree would
mean little consistency or uniformity whereas a low degree of variation would
mean greater uniformity or consistency among the data set. Commonly used measures
of dispersion are range, quartile deviation, mean deviation, variance, and standard
deviation.
Range
The range is the simplest measure
of spread and is the difference between the highest and lowest scores in a data
set. In other words, we can say that the range is the distance between the largest score
and the smallest score in the distribution. We can calculate the range as:
Range = Highest value of the data
– The lowest value of the data
For example, if the lowest and highest marks scored in a test are 22 and 95 respectively, then
Range = 95 – 22 = 73
The range is the easiest measure
of dispersion and is useful when you wish to evaluate the whole of a dataset. However, it is not considered a good measure of dispersion as it does not utilize the
other information related to the spread. The outliers, either extremely low or extremely
high value, can considerably affect the range.
Quartiles
The values that divide the given
set of data into four equal parts are called quartiles and are denoted by Q1,
Q2, and Q3. Q1 is called the lower quartile and Q3
is called the upper quartile. 25% of scores are less than Q1and 75%
scores are less than Q3. Q2 is the median. The formulas
for the quartiles are:
Quartile Deviation (QD)
Quartile deviation or semi
inter-quartile range is one-half the difference between the first and the third
quartile, i.e.
Q D = Q3 – Q1
Where Q1 = the first
quartile (lower quartile)
Q3 = third quartile
(upper quartile)
Calculating quartile deviation
from ungrouped date:
To calculate quartile
deviation from ungrouped data, the following steps are used.
i) Arrange the test scores from highest to
lowest
ii) Assign a serial number to each score. The first
serial number is assigned to the lowest score.
Determine the first quartile (Q1) by using the formula
Use the obtained value to locate the
serial number of the score that falls under Q1.
iv Determine the third (Q3), by using the formula
Locate the serial number corresponding to the
obtained answer. Opposite to this number is the test score corresponding to Q3.
v) Subtract the Q1 from Q3, and divide the difference by 2.
Mean Deviation or Average Deviation
The mean or the average deviation is defined as the arithmetic mean of the deviations of the scores from the mean or the median. The deviations are taken as positive. Mathematically,
Standard Deviation
Standard deviation is the most
commonly used and the most important measure of variation. It determines
whether the scores are generally near or far from the mean, i.e. are the scores
clustered together or scattered. In simple words, standard deviation tells how
tightly all the scores are clustered around the mean in a data set. When the
scores are close to the mean, the standard deviation is small. And large standard
deviation tells that the scores are spread apart. Standard deviation is simply the square root of variance, i.e.
Variance
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