7/30/2019 Relationships Among Means Medians and Modes

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0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9

Frequency

Scores

Mean, Median and Mode in a

Symmetrical Distribution

0

1

2

34

5

6

7

8

1 2 3 4 5 6 7 8 9

Frequency

Scores

Mean, Median and Mode in a

Symmetrical Distribution

0

1

2

3

4

5

6

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1 2 3 4 5 6 7 8 9

Frequency

Scores

Mean, Median and Mode in a

Symmetrical Distribution

RELATIONSHIPS AMONG MEANS, MEDIANS, AND MODES

The most complete information about a distribution is obtained when all three measures of central tendency are

reported. Each provides different kind of information that the teacher may need to better understand class performance.

Measures of Central Tendency summarize the average or typical performance of the class as a whole.

FREQUENCY DISTRIBUTION

SYMMETRICAL LOWER HALF OF THE DISTRIBUTION MIRRORS THE UPPER HALF Figure 1

Mean, median and mode will coincide

Median will lie between the mean and the mode

MEAN = MEDIAN = MODE

Mean = 5.00

Median = 5.00

Mode = 5.00

SKEWEDSCORES ARE PILED UP AT EITHER THE HIGH OR THE LOW END OF DISTRIBUTION, AND THERE IS A TAIL AT THE

OTHER END.

Tail determines whether the distribution is positively skewed or negatively skewed Figure 2

Positively skewedtail is pointed towards the high endMEAN > MEADIAN > MODE

Mean = 3.12 tail

Median = 3.00

Mode = 1.00

Negatively skewedtail is pointed towards the low endMEAN < MEADIAN < MODE Figure 3

Mean = 6.88

Median = 7.00

Mode = 9.00 tail

USE THE MEAN UNDER THE FOLLOWING CONDITIONS:

If sampling is important

If other statistics require or call for a mean

If there are no extreme scores in the distribution or if the teacher wants the extreme scores to play a significant role in

determining central tendency

USE THE MEDIAN UNDER THE FOLLOWING CONDITIONS:

If distributions contain extreme scores, whose effects the teacher wants to minimize.

If the data exist only as ranks.

If a rapid measure of central tendency is required.

USE THE MODE UNDER THE FOLLOWING CONDITIONS:

If the most typical value is desired.

If central tendency must be estimated quickly

SCORES FREQUENCY

9 1

8 2

7 3

6 4

5 5

4 4

3 3

2 2

1 1

SCORES FREQUENCY

9 0

8 1

7 1

6 2

5 2

4 3

3 4

2 5

1 7

SCORES FREQUENCY

9 7

8 5

7 4

6 3

5 2

4 2

3 1

2 1

1 0

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Solutions to Figure 1

Mean = _fx_

n

=__125__

25

=5

Median = 1 2 2 3 3 3 4 4 4 4 5 5 (5) 5 5 6 6 6 6 7 7 7 8 8 9

Mode = 1 2 2 3 3 3 4 4 4 4 (5 5 5 5 5) 6 6 6 6 7 7 7 8 8 9

Solutions to Figure 2

Mean = _fx_

n

=__78__

25

=3.12

Median = 1 1 1 1 1 1 1 2 2 2 2 2 (3) 3 3 3 4 4 4 5 5 6 6 7 8

Mode = (1 1 1 1 1 1 1)2 2 2 2 2 3 3 3 3 4 4 4 5 5 6 6 7 8

Solutions to Figure 3

Mean = _fx_

n

=__172__

25

=6.88

Median = 2 3 4 4 5 5 6 6 6 7 7 7 (7)8 8 8 8 8 9 9 9 9 9 9 9

Mode = 2 3 4 4 5 5 6 6 6 7 7 7 7 8 8 8 8 8 (9 9 9 9 9 9 9)

SCORE

S

FREQUENCY

fx

9 1 9

8 2 16

7 3 21

6 4 24

5 5 254 4 16

3 3 9

2 2 4

1 1 1

n=25 fx =125

SCORES FREQUENCY

fx

9 0 0

8 1 8

7 1 7

6 2 12

5 2 10

4 3 12

3 4 12

2 5 10

1 7 7

n=25 fx=78

SCORES FREQUENCY

fx

9 7 63

8 5 40

7 4 28

6 3 18

5 2 10

4 2 8

3 1 3

2 1 2

1 0 0

n=25 fx=172

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Western Mindanao State University

College of Education

Normal Road, Zamboanga City

A Report in

PED 111(Assessment of Curriculum)

entitled

RELATIONSHIPS AMONG MEAN MEDIAN AND MODE

To be reported by:

LAMATA RONALD SAN JUAN A.K.AANIMEProfessional Education Certificate Student

To be submitted to:

DR. ANNA LOUISA R. PEREZCourse Professor

September 2012