Educ 316 Measuresofcentraltendencyfinal

Marikina Polytechnic College
1st Semester, A.Y. 2015 - 2016
EDUC 316:
ASSESSMENT OF
LEARNING I
MEASURES OF
CENTRAL TENDENCY
MEASURE OF CENTRAL TENDENCY
The measure of central tendency
is populary known as an average,
where as ingle central value can
stand for the entire group of figures
as typical of all the values in the
group, these are:
1. Mean
2. Median
3. Mode
MEAN
Mean is the most frequently used

measure of central tendency
because it is subject to less error; it
is also easily calculated.
MEAN
ADVANTAGE DISADVANTAGE
 best measure for  does not supply
regular distribution information about the
homogeneity of the
group
The ARITHMETIC MEAN
The symbol X , called “X bar” is used

to represent the mean of a sample and
the symbol  , called “mu”, is used to
denote the mean of a population.
Mean of Ungrouped Data
X 1  X 2  X 3  ...  X k
X 
N
Sum of all the scores
Mean 
Number of scores or cases
Mean of Ungrouped Data
X
 X
N
where:
X  Arithmetic mean
 X  Sum of all the scores
N  Number of scores or cases
The WEIGHTED MEAN
The weighted mean is applicable

to options of different weights. It is
found by multiplying each value by
its corresponding weight and
dividing by the sum of weights.
Weighted Mean
f1 X 1  f 2 X 2  f3 X 3  ...  f k X k
Xf 
f1  f 2  f3  ...  f k
where: X f  weighted mean
 fX  Sum of all the products of f and X
where f is the frequency of each score
and X , weight of each score
f  Sum of all the respondents tested
observations
Samples of 30 college students are
considered for study with Math quiz score
out of 20 points. Compute the mean,
median, and mode of the data.
18 14 12 10 9 7
18 13 12 10 8 7
17 13 11 10 8 6
16 12 11 10 8 5
15 12 11 9 8 3
Mean of Grouped Data
X 
 fM
N
Sum of all the product of

midpoint times frequency
Mean 
Total number of cases
Step 1: Compute the midpoints of all class
limits which is given the symbol M.
Step 2: Multiply each midpoint by the
corresponding frequency.
Step 3: Sum of the product of midpoints times
frequencies.
Step 4: Divide this sum by the total number of
cases (N) to he obtain mean.
Construct a frequency distribution and
compute the mean, median and mode of
the data.
18 14 12 10 9 7
18 13 12 10 8 7
17 13 11 10 8 6
16 12 11 10 8 5
15 12 11 9 8 3
The sum of absolute deviations
(disregard the sign) ∑d about the
median is less than or equal to the sum
of absolute deviations about any other
value.
Median is consistent in type with other
point measures such as the quartile,
decile, and percentile.
 best measure of  necessitates
central tendency when arranging of items
the distribution is according to size
irregular or skewed. before it can be
computed
To determine the value of median for
ungrouped data, we need to consider two
rules:
1. If n is odd, the median is the middle
ranked.
2. If n is even, then the median is the
average of two middle ranked values.
Note that n the population/sample size.
(n  1)
Median ( Ranked Value) =
2
Note that n is the population/sample size.
The median is located in the middle
value of the frequency distribution. It is the
value that separates the upper half of the
distribution from the lower half. It is also a
measure of central tendency because it is
the exact center of the scores in a
distribution.
N 
 2   C f 
x% LC 
where:  fC 
°
X  median
L  lower real limit of the median class
N  total number of cases
 Cf   sum of the cumulative frequencies "lesser than"
up to but below the median class
fC  frequency of the median class
C  class interval
It is the value in a data set that
appears most frequently. In a data
set, extreme values do not affect
the mode. A data may not contain
any mode if none of the values is
“most typical”.
 always a real  inapplicable to
value since it does small number of
not fall on zero cases when the
values may not be
repeated
A data set that has only one value that
occurs with the greatest frequency is said to
be unimodal.
If a data set has two values that occur with
the same greatest frequency, both values are
considered to be the mode and the data set
is said to be bimodal.
If a data set has more than two
values that occur with the same
greatest frequency, each value is
used as the mode, and the data
set is said to be multimodal.
When no data value occurs more
than once, the data set is said to
have no mode.
µ C  f1  f 2 
X  Lmo   
2  2 f 0  f 2  f1 
where:
µ
X  mode
L  lower class limit of modal class
f1  frequency of the class after the modal class
f 2  frequency of the class before the modal class
f 0  frequency of the modal class
C  class interval

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Marikina Polytechnic College

1st Semester, A.Y. 2015 - 2016

Mean is the most frequently used

The symbol X , called “X bar” is used

The weighted mean is applicable

Sum of all the product of

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