Measures Of Central Tendency for
Ungrouped Data
Source: https://www.google.com/search?q=picture+of+mean+,
+median+and+mode&tbm
MEASURES OF CENTRAL TENDENCY:
It is a statistic that serves as a representative of the data under investigation.
This tends to lie within the center of the set of data.
There are three measures of central tendency such as the arithmetic mean( simply
mean ), median, and mode.
The Mean
It is the most important, the most useful, and the most widely used measure of
central tendency.
It refers to the sum of all the given values or items in a distribution divided by the
number of values or items summed.
Mean has limitations and uses.
The Mean is Used
for interval and ratio measurement;
If higher statistical computations are wanted;
, If there are no extreme values in the distribution since it is easily affected by
extremely low scores or extremely high scores. Thus, the distribution is
approximately normal;
When the greater reliability of the measure of central tendency is wanted since its
computations include all the given values.
The Limitations of the Mean
It is the most widely used average because it is the most familiar. It is often,
however, misused. It cannot be used in the clustering of values or items that are not
substantial. An example is when representing the scores or values, 10 and 100
since they are far apart.
When the given values do not tend to cluster around a central value, the mean is a
poor measure of central location.
It is easily affected by extremely large or small values. One small value can easily
pull down the mean.
The mean cannot be utilized to compare distributions since the means of two or
more distributions may be the same but their characteristics may be entirely
different. The means of distribution A whose values are 80, 85, and 90, and
distribution B whose values are 86, 85, and 84 are both 85.
However, we cannot imply that both distributions possess the same characteristics
since their patterns of dispersion or variations are markedly different despite having the
same mean.
Arithmetic Mean ( denoted by ) or simply mean is the sum of all
values in a data set divided by the number of values that are summed. It is written
mathematically:
The following formulas are used for Ungrouped Data:
Sample Mean: =∑xn=∑xn
where: = mean
x = is the individual value
n = total number of values
∑x=∑x=the sum of all x's
Population Mean: μ=μ=∑xN∑xN
where: μ=μ=population mean
x = is the individual value
N = total number of values in a population
Ungrouped Data
Source: https://www.google.com/search?q=picture+of+mean+,
+median+and+mode&tbm
MEASURES OF CENTRAL TENDENCY:
It is a statistic that serves as a representative of the data under investigation.
This tends to lie within the center of the set of data.
There are three measures of central tendency such as the arithmetic mean( simply
mean ), median, and mode.
The Mean
It is the most important, the most useful, and the most widely used measure of
central tendency.
It refers to the sum of all the given values or items in a distribution divided by the
number of values or items summed.
Mean has limitations and uses.
The Mean is Used
for interval and ratio measurement;
If higher statistical computations are wanted;
, If there are no extreme values in the distribution since it is easily affected by
extremely low scores or extremely high scores. Thus, the distribution is
approximately normal;
When the greater reliability of the measure of central tendency is wanted since its
computations include all the given values.
The Limitations of the Mean
It is the most widely used average because it is the most familiar. It is often,
however, misused. It cannot be used in the clustering of values or items that are not
substantial. An example is when representing the scores or values, 10 and 100
since they are far apart.
When the given values do not tend to cluster around a central value, the mean is a
poor measure of central location.
It is easily affected by extremely large or small values. One small value can easily
pull down the mean.
The mean cannot be utilized to compare distributions since the means of two or
more distributions may be the same but their characteristics may be entirely
different. The means of distribution A whose values are 80, 85, and 90, and
distribution B whose values are 86, 85, and 84 are both 85.
However, we cannot imply that both distributions possess the same characteristics
since their patterns of dispersion or variations are markedly different despite having the
same mean.
Arithmetic Mean ( denoted by ) or simply mean is the sum of all
values in a data set divided by the number of values that are summed. It is written
mathematically:
The following formulas are used for Ungrouped Data:
Sample Mean: =∑xn=∑xn
where: = mean
x = is the individual value
n = total number of values
∑x=∑x=the sum of all x's
Population Mean: μ=μ=∑xN∑xN
where: μ=μ=population mean
x = is the individual value
N = total number of values in a population
