Measures of Central Tendency

Central Tendency What is Central Tendency? Central tendency of a data set is a measure of the “middle” or “expected” value of data set.

Why Central Tendency is needed? Due to the following aspects central tendency is needed: •

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Central tendency gives us simple and brief description of the main features of the whole data. The measures of central tendency or averages reduce the data to a single value which is highly useful for making comparative studies. Other statistical devices such as mean deviation co-efficient of variation, corelation, analysis of time series and index numbers are also based on the central tendency; and hence the use of central tendency becomes compulsory.

Measures of Central Tendency: Measure of central tendency means measure of center of  data. Followings are the measures of central tendency: Mean ------ average of data Median ---- central value of data Mode ------ most repeated value of data

Mean: The arithmetic average represents the most appropriate measure of central tendency for continuous-type data. It is obtained by adding all of the scores and dividing this sum by the number of scores. Mean (  X  ) =

Σ X   N 

Where the mean can be denoted by  X  (pronounced”X-bar”) for samples; ∑ denotes summation of a set of values; X represents the individual raw scores, and N equals the number of scores.

Advantages & Disadvantages of Mean: Advantages:• • •

Mathematical center of a distribution. Good for interval and ratio data. Does not ignore any information.

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Inferential statistics is based on mathematical properties of the mean.

Disadvantages:• •

Influenced by extreme scores and skewed distribution. May not exist in the data.

Median: The median of a set of scores represents the middle value when the scores are arranged as an array in order of increasing or decreasing magnitude. To locate the median, first rank the scores and follow these two guidelines: 1. For an odd number of scores, the median is the middle score. 2. For an even number of scores, the median is the mean (arithmetic average) of the two middle scores.

Advantages and Disadvantages of Median: Advantages:• • • •

 Not influenced by extreme scores or skewed distribution. Good with original data. Easier to compute than the mean. Considered as the typical observation.

Disadvantages:• •

May not exist in the data. Does not take actual values into account.

Mode: The mode represents the most frequently occurring score. When two scores occur  with the same greatest frequency, each one equals the mode and the data set is considered  bimodal. When more than two score occur with the greatest frequency, the data set is said to be multimodal.

Advantages and Disadvantages of Mode: Advantages:• • •

Good with nominal data. Easy to compute and understand. The score exist in the data set.

Disadvantages:• • •

Ignore most of the information in a distribution. Small samples may not have a mode. More than one mode might exist.

Objectives and Functions of Averages or Central Tendency: •

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The human mind cannot retain all details of large number of activities and their  inter-relations, so averages are a must. An average represents all the features of a group hence the results about the whole group can be deduced from it. An average gives us simple and brief description of the main features of the whole data. The measures of central tendency or averages reduce the data to a single value which is highly useful for making comparative studies. Averages help to develop a business in case of a firm or help the economy of a country to develop. For example, in case of an aviation company, the management will be interested to know about the average number of persons  boarding plane on the desired certain route. In such a case, a finance minister or  finance secretary would apply some economic measures to increase per capital income if he feels that it is lower as compared to other developed country's per  capital income. Other statistical devices such as mean deviation co-efficient of variation, corelation, analysis of time series and index numbers are also based on the averages; and hence the use of averages becomes compulsory.