measure of central tendency

MEASURE OF CENTRAL TENDENCY

Single value in series of observation which indicate the characteristics of observation.

All data/values clustered around it and used to compare between one series to another.

Measures:

         a. Mean  (Arithmetic/ Geometric/Harmonic)

                 b. Median

                 c. Mode

MEDIAN

Median is what divides the scores in the distribution into two equal parts.

Fifty percent(50%) lies below the median value and 50% lies above the median value.

It is also known as the middle score or 50th percentile.

MEDIAN OF UNGROUPED DATA

•Arrange the scores(from lowest to highest or highest to lowest)

•Determine the middle score in a distribution if n is an odd number and get the average of the two middle most scores if n is an even number.

EXAMPLE

•Find the median score of 7 students in an English class.

                               x(score)

                                  19

                                  17

                                  16

                                  15

                                  10

                                   5

                                   2

 MEDIAN OF GROUPED DATA

Formula:

        Median= l + ( (n/2-m)/f)*c

Where l=Lower limit of the median class

             f=Frequency of the median class

             c=Width of the median class

             N=The total frequency

             m=cumulative frequency of the class

                   preceeding the median class

                PROPERTIES OF MEDIAN

•It may not be an actual observation in the data set.

•It can be applied in ordinal level.

•It is not affected by extreme values because median is a positional measure.

  APPLICATION OF MEDIAN

•It is used to measure the distribution of the earning.

•Use to find the players height e.g.  Football players.

•To find the middle age from the classroom students.

•Also used to find the poverty line.

MODE

The mode or the modal score is a score or scores that occurs in the distribution.

It is classified as unimodal,  bimodal, trimodal or multimodal.

CLASSIFICATION OF MODE

•Unimodal is a distribution of scores that consists of only one mode.

•Bimodal is a distribution of scores that consist of two modes.

•Trimodal is a distribution of scores that consist of three modes or multimodal is a distribution of scores that consist of more than two modes.

MODE FOR GROUPED DATA

Formula:

      Mode= l+     (  f-f1  /2f-f1-f2) *c

Where l=lower limit of the modal class

             f=frequency of modal class

             c=class width of the modal class

             f =frequency of the class just preceeding the

                  modal class

             f2=frequency of the class succedding the

                   modal class

PROPERTIES OF MODE

•It can be used when the data are qualitative as well as quantitative.

•It may not be unique.

•It is affected by extreme values.

It may not exist

APPLICATION OF MODE

•It is used to influx of the public transport.

•The number of games succeeded by any team of players.

•The frequency of the need of infants.

•Used to find the number of the mode is also seen in calculation of the wages,  in the patients going to the hospitals, mode of travels, etc.,

CONCLUSION

• A measure of central tendency is a measure tell us where the middle of a bunch of data lies.

•Median is the number of present in the middle when the number in a set of data are arranged in ascending or descending order.

•Mode is the value that occurs most frequently in a set of data.