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FLORINDA M SOLIMAN TEACHER II TAGAYTAY CITY SCIENCE NATIONAL HIGH SCHOOL

Measures of Central Tendency

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Measures of Central Tendency. FLORINDA M SOLIMAN TEACHER II. TAGAYTAY CITY SCIENCE NATIONAL HIGH SCHOOL. Measures of Central Tendency. A measures of central tendency may be defined as single expression of the net result of a complex group. - PowerPoint PPT Presentation

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Page 1: Measures of           Central Tendency

FLORINDA M SOLIMAN TEACHER II

TAGAYTAY CITY SCIENCE NATIONAL

HIGH SCHOOL

Page 2: Measures of           Central Tendency

A measures of central tendency may be defined as single expression of the net result of a complex group.

There are two main objectives for the study of measures of Central Tendency.

To facilitate comparison

To get one single value that represents the entire data.

Page 3: Measures of           Central Tendency

There are three averages or measures of central tendency

Mean

Median

Mode

Page 4: Measures of           Central Tendency

Mean/Arithmetic Mean The most commonly used and familiar index of

central tendency for a set of raw data or a distribution is the mean

The mean is simple Arithmetic Average

The arithmetic mean of a set of values is their sum divided by their number

Page 5: Measures of           Central Tendency

MERITS OF THE USE OF MEAN

It is easy to understand

It is easy to calculate

It utilizes entire data in the group

It provides a good comparison

It is rigidly defined

Page 6: Measures of           Central Tendency

Limitations

Abnormal difference between the highest and the lowest score would lead to fallacious conclusions

In the absence of actual data it can mislead

Its value cannot be determined graphically

A mean sometimes gives such results as appear almost absurd. e.g. 4.3. children

Page 7: Measures of           Central Tendency

Steps in Constructing Frequency Distribution Table

1. Range = Highest Score – Lowest Score

2. Class Width =

Page 8: Measures of           Central Tendency

49

4844

4746

44

4640

4340

40

4241

4136

36

3637

3738

38

3939

3932

32

3232

3333

33

3435

34

35

28

28

28

2929

29

2929

3030

25

2424

2525

26

2727

2021

22

2321

2222

23

2316

1617

19

1213

1415

12

8 8 8 8 9 10 7 7 7

49

4844

4746

44

4640

4340

40

4241

4136

36

3637

3738

38

3939

3932

32

3232

3333

33

3435

34

35

28

28

28

2929

29

2929

3030

25

2424

2525

26

2727

2021

22

2321

2222

23

2316

1617

19

1213

1415

12

8 8 8 8 9 10 7 7 7

Page 9: Measures of           Central Tendency

CLASS INTERVALS ( CI ) FREQUENCY ( F )

n 80

48 – 51

n 80

44 – 47

80

40 – 43

80

36 – 39

80

32 – 35

n 80

28 – 31

80

24 – 27

80

20 – 23

80

16 – 19

n 80

12 – 15

80

8 – 11

n 80

4 – 7

n 80

Page 10: Measures of           Central Tendency

CLASS INTERVALS ( CI ) FREQUENCY ( F )

n 80

48 – 512

n 80

44 – 47 5

40 – 43 7

80

36 – 39 10

80

32 – 35 11

n 80

28 – 31 10

80

24 – 27 8

80

20 – 23 9

80

16 – 19 4

n 80

12 – 15 5

80

8 – 11 6

n 80

4 – 7 3

n 80

Page 11: Measures of           Central Tendency

Calculation for Mean

Page 12: Measures of           Central Tendency

Calculation of Arithmetic MeanFor Group DataAssume mean Method:

Mean = AM +

Page 13: Measures of           Central Tendency

Calculation of Arithmetic MeanFor Group Data

X = midpoint

AM = Assumed Mean

i = Class Interval size

fd = Product of the frequency and the

corresponding deviation

Page 14: Measures of           Central Tendency

Class Intervals

( CI )

Frequency ( F )

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4

12 – 15 5

8 – 11 6

4 - 7 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4

12 – 15 5

8 – 11 6

4 - 7 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4

12 – 15 5

8 – 11 6

4 - 7 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4

12 – 15 5

8 – 11 6

4 - 7 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4

12 – 15 5

8 – 11 6

4 - 7 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4

12 – 15 5

8 – 11 6

4 - 7 3

Total 80

Page 15: Measures of           Central Tendency

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4

12 – 15 5

8 – 11 6

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4

12 – 15 5

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 – 23 9

16 – 19 4

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2

44 – 47 5

40 – 43 7 73

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52

44 – 47 5 78

40 – 43 7 73

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80

44 – 47 5 78

40 – 43 7 73

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Page 16: Measures of           Central Tendency

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80

44 – 47 5 78

40 – 43 7 73

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78

40 – 43 7 73

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45 29.5

24 – 27 8 35

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45 29.5

24 – 27 8 35 25.5

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45 29.5

24 – 27 8 35 25.5

20 - 23 9 27 21.5

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45 29.5

24 – 27 8 35 25.5

20 - 23 9 27 21.5

16 – 19 4 18 17.5

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45 29.5

24 – 27 8 35 25.5

20 - 23 9 27 21.5

16 – 19 4 18 17.5

12 – 15 5 14 13.5

8 – 11 6 9

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45 29.5

24 – 27 8 35 25.5

20 - 23 9 27 21.5

16 – 19 4 18 17.5

12 – 15 5 14 13.5

8 – 11 6 9 9.5

4 - 7 3 3

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45 29.5

24 – 27 8 35 25.5

20 - 23 9 27 21.5

16 – 19 4 18 17.5

12 – 15 5 14 13.5

8 – 11 6 9 9.5

4 - 7 3 3 5.5

Total 80

Page 17: Measures of           Central Tendency

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5

44 – 47 5 78 45.5

40 – 43 7 73 41.5

36 – 39 10 66 37.5

32 – 35 11 56 33.5

28 – 31 10 45 29.5 0

24 – 27 8 35 25.5

20 - 23 9 27 21.5

16 – 19 4 18 17.5

12 – 15 5 14 13.5

8 – 11 6 9 9.5

4 - 7 3 3 5.5

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5 5

44 – 47 5 78 45.5 4

40 – 43 7 73 41.5 3

36 – 39 10 66 37.5 2

32 – 35 11 56 33.5 1

28 – 31 10 45 29.5 0

24 – 27 8 35 25.5

20 - 23 9 27 21.5

16 – 19 4 18 17.5

12 – 15 5 14 13.5

8 – 11 6 9 9.5

4 - 7 3 3 5.5

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5 5

44 – 47 5 78 45.5 4

40 – 43 7 73 41.5 3

36 – 39 10 66 37.5 2

32 – 35 11 56 33.5 1

28 – 31 10 45 29.5 0

24 – 27 8 35 25.5 -1

20 - 23 9 27 21.5 -2

16 – 19 4 18 17.5 -3

12 – 15 5 14 13.5 -4

8 – 11 6 9 9.5 -5

4 - 7 3 3 5.5 -6

Total 80

Page 18: Measures of           Central Tendency

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’

48 – 52 2 80 49.5 5

44 – 47 5 78 45.5 4

40 – 43 7 73 41.5 3

36 – 39 10 66 37.5 2

32 – 35 11 56 33.5 1

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1

20 - 23 9 27 21.5 -2

16 – 19 4 18 17.5 -3

12 – 15 5 14 13.5 -4

8 – 11 6 9 9.5 -5

4 - 7 3 3 5.5 -6

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5 5 10

44 – 47 5 78 45.5 4 20

40 – 43 7 73 41.5 3 21

36 – 39 10 66 37.5 2 20

32 – 35 11 56 33.5 1 11

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1

20 - 23 9 27 21.5 -2

16 – 19 4 18 17.5 -3

12 – 15 5 14 13.5 -4

8 – 11 6 9 9.5 -5

4 - 7 3 3 5.5 -6

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5 5 10

44 – 47 5 78 45.5 4 20

40 – 43 7 73 41.5 3 21

36 – 39 10 66 37.5 2 20

32 – 35 11 56 33.5 1 11

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1 -8

20 - 23 9 27 21.5 -2 -18

16 – 19 4 18 17.5 -3 -12

12 – 15 5 14 13.5 -4 -20

8 – 11 6 9 9.5 -5 -30

4 - 7 3 3 5.5 -6 -18

Total 80

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5 5 10

44 – 47 5 78 45.5 4 20

40 – 43 7 73 41.5 3 21

36 – 39 10 66 37.5 2 20

32 – 35 11 56 33.5 1 11

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1 -8

20 - 23 9 27 21.5 -2 -18

16 – 19 4 18 17.5 -3 -12

12 – 15 5 14 13.5 -4 -20

8 – 11 6 9 9.5 -5 -30

4 - 7 3 3 5.5 -6 -18

Total 80 -24

Page 19: Measures of           Central Tendency

Class Intervals

( CI )

Frequency ( F ) <Cf Mdpt d’ fd’

48 – 52 2 80 49.5 5 10

44 – 47 5 78 45.5 4 20

40 – 43 7 73 41.5 3 21

36 – 39 10 66 37.5 2 20

32 – 35 11 56 33.5 1 11

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1 -8

20 - 23 9 27 21.5 -2 -18

16 – 19 4 18 17.5 -3 -12

12 – 15 5 14 13.5 -4 -20

8 – 11 6 9 9.5 -5 -30

4 - 7 3 3 5.5 -6 -18

Total 80 -24

Page 20: Measures of           Central Tendency
Page 21: Measures of           Central Tendency

Calculation for Median

Page 22: Measures of           Central Tendency

Median

When all the observation of a variable are arranged in either ascending or descending order the middles observation is Median. It divides the whole data into equal proportion. In other words 50% observations will be smaller than the median and 50% will be larger than it.

Page 23: Measures of           Central Tendency

Merits of Median

Like mean, Median is simple to understand

Median is not affective by extreme items

Median never gives absurd or fallacious result

Median is specially useful in qualitative

phenomena

Page 24: Measures of           Central Tendency

Median = L +

Where,L = exact lower limit of the Cl in which

Median lies

F = Cumulative frequency up to the lower limit of the Cl containing Median

fm = Frequency of the Cl containing median

i = Size of the class intervals

Page 25: Measures of           Central Tendency

Class Intervals( CI )

Frequency ( F )<Cf

48 – 52 2 80

44 – 47 5 78

40 – 43 7 73

36 – 39 10 66

32 – 35 11 56

28 – 31 10 45

24 – 27 8 35F

20 - 23 9 27

16 – 19 4 18

12 – 15 5 14

8 – 11 6 9

4 - 7 3 3

Total 80

28 – 31 10 45

35F

10 fm

Page 26: Measures of           Central Tendency

Median = L +

Here; L = 27.5 F = 35 fm =10

= 27.5 + (40 – 35) 10 4

= 27.5 + 2

= 29.5

Page 27: Measures of           Central Tendency

MARILOU M. MARTINTEACHER - 1

IMUS NATIONAL HIGH SCHOOL

Page 28: Measures of           Central Tendency

The goal for variability is to obtain a measure

of how spread out the scores are in a distribution.

A measure of variability usually accompanies

a measure of central tendency as basic

descriptive statistics for a set of scores.

Page 29: Measures of           Central Tendency

Central tendency describes the central point

of the distribution, and variability describes

how the scores are scattered around that central point.

Together, central tendency and variability are

the two primary values that are used to describe a distribution of scores.

Page 30: Measures of           Central Tendency

Variability serves both as a descriptive measure and as an important component of most inferential statistics.

As a descriptive statistic, variability measures the degree to which the scores are spread out or clustered together in a distribution.

In the context of inferential statistics, variability provides a measure of how accurately any individual score or sample represents the entire population.

Page 31: Measures of           Central Tendency

When the population variability is small, all of the scores are clustered close together and any individual score or sample will necessarily provide a good representation of the entire set. On the other hand, when variability is large and scores are widely spread, it is easy for one or two extreme scores to give a distorted picture of the general population.

Page 32: Measures of           Central Tendency

Variability can be measured with the rangethe interquartile rangethe standard deviation/variance.

In each case, variability is determined by measuring distance.

Page 33: Measures of           Central Tendency

Standard deviation measures the standard distance between a score and the mean. The calculation of standard

deviation can be summarized as a four-step process:

Page 34: Measures of           Central Tendency

1. Compute the deviation (distance from the mean) for each score.

2. Solve for the product of frequency and deviation and solve for the total frequency deviation.

Page 35: Measures of           Central Tendency

3. Compute for the sum of the product of frequency deviation square.(fd’²)

Page 36: Measures of           Central Tendency

Class Intervals

( CI )

Frequency ( F ) <Cf

Mdpt

d’ fd’ (fd’)²

48 – 52 2 80 49.5 5 10

44 – 47 5 78 45.5 4 20

40 – 43 7 73 41.5 3 21

36 – 39 10 66 37.5 2 20

32 – 35 11 56 33.5 1 11

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1 -8

20 - 23 9 27 21.5 -2 -18

16 – 19 4 18 17.5 -3 -12

12 – 15 5 14 13.5 -4 -20

8 – 11 6 9 9.5 -5 -30

4 - 7 3 3 5.5 -6 -18

Total 80 -24

Class Intervals

( CI )

Frequency ( F ) <Cf

Mdpt

d’ fd’ (fd’)²

48 – 52 2 80 49.5 5 10 50

44 – 47 5 78 45.5 4 20

40 – 43 7 73 41.5 3 21

36 – 39 10 66 37.5 2 20

32 – 35 11 56 33.5 1 11

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1 -8

20 - 23 9 27 21.5 -2 -18

16 – 19 4 18 17.5 -3 -12

12 – 15 5 14 13.5 -4 -20

8 – 11 6 9 9.5 -5 -30

4 - 7 3 3 5.5 -6 -18

Total 80 -24

Class Intervals

( CI )

Frequency ( F ) <Cf

Mdpt

d’ fd’ (fd’)²

48 – 52 2 80 49.5 5 10 50

44 – 47 5 78 45.5 4 20 80

40 – 43 7 73 41.5 3 21

36 – 39 10 66 37.5 2 20

32 – 35 11 56 33.5 1 11

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1 -8

20 - 23 9 27 21.5 -2 -18

16 – 19 4 18 17.5 -3 -12

12 – 15 5 14 13.5 -4 -20

8 – 11 6 9 9.5 -5 -30

4 - 7 3 3 5.5 -6 -18

Total 80 -24

Class Intervals

( CI )

Frequency ( F ) <Cf

Mdpt

d’ fd’ (fd’)²

48 – 52 2 80 49.5 5 10 50

44 – 47 5 78 45.5 4 20 80

40 – 43 7 73 41.5 3 21 63

36 – 39 10 66 37.5 2 20

32 – 35 11 56 33.5 1 11

28 – 31 10 45 29.5 0 0

24 – 27 8 35 25.5 -1 -8

20 - 23 9 27 21.5 -2 -18

16 – 19 4 18 17.5 -3 -12

12 – 15 5 14 13.5 -4 -20

8 – 11 6 9 9.5 -5 -30

4 - 7 3 3 5.5 -6 -18

Total 80 -24

Class Intervals

( CI )

Frequency ( F ) <Cf

Mdpt

d’ fd’ (fd’²)

48 – 52 2 80 49.5 5 10 50

44 – 47 5 78 45.5 4 20 80

40 – 43 7 73 41.5 3 21 63

36 – 39 10 66 37.5 2 20 40

32 – 35 11 56 33.5 1 11 11

28 – 31 10 45 29.5 0 0 0

24 – 27 8 35 25.5 -1 -8 8

20 - 23 9 27 21.5 -2 -18 36

16 – 19 4 18 17.5 -3 -12 36

12 – 15 5 14 13.5 -4 -20 80

8 – 11 6 9 9.5 -5 -30 150

4 - 7 3 3 5.5 -6 -18 108

Total 80 -24 662

Page 37: Measures of           Central Tendency

SD =

SD =

SD = 4 ( 2.879) = 11.52

Page 38: Measures of           Central Tendency

SHIRLEY PEL – PASCUALMaster Teacher – I

GOV. FERRER MEMORIAL NATIONAL HIGH SCHOOL

Page 39: Measures of           Central Tendency

Mean scores are used to determine the average performances of students or athletes, and in

various other applications. Mean scores can be converted to percentages that indicate the average percentage of the score relative to the total score.

Page 40: Measures of           Central Tendency

Mean scores can also be converted to percentages to show the performance of a score relative to a specific score. For instance, a mean score can be compared to the highest score with a percentage for a better comparison. Percentages can be useful means of statistical analysis.

Page 41: Measures of           Central Tendency
Page 42: Measures of           Central Tendency

Instructions

1.Find the mean score if not already determined.

The mean score can be determined by adding

up all the scores and dividing it by "n," the number of scores.

Page 43: Measures of           Central Tendency

Instructions

2 Determine the score that you want to compare the mean score to. You may compare the mean score with the highest possible score, the highest score, or a specific score.

Page 44: Measures of           Central Tendency

Instructions

3. Divide the mean score by the score you decided to use in step 2.

Page 45: Measures of           Central Tendency

Instructions

4. Multiply the decimal you obtain in step 3 by 100, and add a % sign to obtain the percentage. You may choose to round the percentage to the nearest whole number.