Measures of Central Tendency(Mode, Median, Mean)




Averages:

Mode:

Mode is a most often occurring value in a distribution .

I)The most numerous category

II)For ratio data, often implies that data have been grouped in some way. It can be more or less created by the grouping procedure

III)For theoretical distributions – simply the location of the peak on the frequency distribution.

Advantages :

I)Quick and easy to compute

II)Unaffected by extreme scores unrepresentative

III)Can be used at any level of measurement

Disadvantages:

I)Terminal statistics

II)A given sub group cloud make this measure

Mean:

Arithmetic average the sum of all values in a distribution divided by the number of cases

I) Center of gravity

II)Even partitions the sum of all measurement among all cases, an average of all measures

Advantages and Disadvantages:

I) Crucial for inferential statistics

II) Mean is not very resistant to outliers

III) A “trimmed mean” may be better for descriptive purposes

R: mean(x)

Arithmetic mean, Harmonic mean, Geometric mean, also f- mean, truncated mean, power mean, weighted mean, etc.

Median :

midpoint in the distribution below which half of the cases reside.

I)less useful for inferential purposes

II)more resistant to the effects of outliers.

The mean or average of data values is

mean = sum of all data values/ number of data values

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