This document discusses measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of items. The median is the middle value when items are arranged from lowest to highest. The mode is the value that occurs most frequently in a data set. Examples are given to demonstrate calculating each measure using raw data.

1. EDUC 316:
ASSESSMENT OF
LEARNING I
MEASURES OF
CENTRAL TENDENCY
Marikina PolytechnicCollege
1st Semester, A.Y. 2015 - 2016

2. 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

3. MEAN
Mean is the most frequently used
measure of central tendency
because it is subject to less error; it
is also easily calculated.

4. MEAN
ADVANTAGE DISADVANTAGE
 best measure for
regular distribution
 does not supply
information about the
homogeneity of the
group

5. The ARITHMETIC MEAN
The symbol , 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.

X

6. Mean of Ungrouped Data
Mean 
Sum of all the scores
Number of scores or cases
1 2 3 ... kX X X X
X
N
   


7. where:
Mean of Ungrouped Data
X
X
N


Arithmetic mean
Sum of all the scores
Number of scores or cases
X
X
N





8. 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.
The WEIGHTED MEAN

9. Weighted Mean
1 1 2 2 3 3
1 2 3
...
...
k k
f
k
f X f X f X f X
X
f f f f
   

   
where: weighted mean
Sum of all the products of and
where is the frequency of each score
and , weight of each score
Sum of all the respondents tested
observations
fX
fX f X
f
X
f






10. 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
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.

11. Mean of Grouped Data
Mean 
Sum of all the product of
midpoint times frequency
Total number of cases
fM
X
N



12. 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.

13. 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
Construct a frequency distribution and
compute the mean, median and mode of
the data.

14. 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.

15. ADVANTAGE DISADVANTAGE
 best measure of
central tendency when
the distribution is
irregular or skewed.
 necessitates
arranging of items
according to size
before it can be
computed

16. 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.

17. ( 1)
Median ( Ranked Value) =
2
Note that is the population/sample size.
n
n


18. 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.

19. ° median
lower real limit of the median class
otal number of cases
um of the cumulative frequencies "lesser than"
up to but below the median class
frequency of the median class
cla
X
L
N t
Cf s
fC
C








ss interval
% 2
N
C f
x L C
f C

 
 
   
 

where:

20. 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”.

21. ADVANTAGE DISADVANTAGE
 always a real
value since it does
not fall on zero
 inapplicable to
small number of
cases when the
values may not be
repeated

22. 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.

23. 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.

24. µ 1 2
0 2 12 2
mo
f fC
X L
f f f
 
   
  
µ
1
2
0
mode
lower class limit of modal class
frequency of the class after the modal class
frequency of the class before the modal class
frequency of the modal class
class interval
X
L
f
f
f
C






where: