measures of central tendencies

Measures of central tendencies

Quantitative data of large numbers generally exhibit a common characteristics that they have a tendency to concentrate at certain values usually somewhere in the centre of the distribution. Such concentration of items in the central part of the distribution is known as central tendencies.

Arithmetic mean

Merits

1.      Mean is the average value of scores be easily calculated using mathematical methods.

2.      Mean is a central tendency, the deviation on either side of which is equal.

3.      Mean is very sensitive, change in any obtained score of the group can change it, so it is considered to be the real representative of scores of any group.

4.      Mean is more reliable than other central tendencies.

Demerits

1.      Mean represents the score of a group only, when the distribution of scores is normal.

2.      Mean represents the scores of a group only in the condition when the scores are homogeneous.

3.      It can be used only in that condition when the data are given on interval scale or in the form of scores.

Utility and importance of mean in education

1.      when midpoint of scores of a group is to be known.

2.      When the scores of a group are to be evaluated according to their value

3.      When the scores of 2/more groups are to be compared.

4.      When deviation or co-efficient of correlation of the scores have to be calculated.

5.      It is needed in educational research

Median

Median is a central tendency which divides the scores of a group into two equal parts. In such a way the scores of one part are more than it and the scores of another part is less than it.

Merits

1.      Median is the exact mid value of scores of a group arranged in rank order. So it is suitable for comparison and analysis of other scores in the group.

2.      When deviation of scores of a group is abnormal or the value of some scores is too large or too low as compared to other scores, then median is more useful than mean

3.      Median is more useful for qualitative analysis of scores of a group as compared to other central tendencies.

4.      The median displayed by a groups in graph can also be used to analysis the scores of other groups by median.

Limitation

1.      Median can be found out for the scores of a group and not for the scores of two groups.

2.      Median is a fixed value of scores of a group, so it is necessary to arrange all scores in rank order. In case of a large group, it requires more time and energy.

Utility in education

1.      When the distribution of scores of a group is not normal

2.      When all scores of a group are not received.

3.      When we have to find out the situation of a particular person in a group, whether he comes in the first 50% or last 50%.

4.      It is necessary for research purpose.

Mode   (the highest frequency of scores)

Merits

1.      Mode is any given scores od a group can be easily find out, including the abnormal scores.

2.      Mode of a score of a group can be found out by graph also. It is that part, the height of which in the frequency curve is tallest.

3.      When the value of scores of a group are too high or too low as compared to other scores in the group, even in that situation, mode is not affected

4.      Mode is more useful for qualitative analysis of scores of a group.

Limitations

1.      When no score is in mode the two or more scores with high difference come under the category of mode, in such situation mode is meaningless.

2.      Mode is a guessed central tendency, so it is less useful for statistical calculations