The most common measures of central tendency are mean, median, and mode. The RANGE is also used to describe a set of data.

Mean, mode and median are measures of central tendency (that is, the centre or middle of a set of data) and provide a single representative or typical value in a distribution.

Mean, median and mode are all measures of central tendencies.

Standard deviation is not a measure of Central tendency.

Terms in this set (21) The three measures are: mode, median, and mean. a variable is computed by determining the sum of all the values of the variable in the data set and dividing by the number of observations.

Central tendency indicates the middle or average of a distribution and provides a single score to represent the entire set of scores.

The purpose of central tendency is to find a single value that best represents an entire distribution of scores. Identify the circumstances where the median instead of the mean is the preferred measure of central tendency.

The preferred measure of central tendency often depends on the shape of the distribution. Of the three measures of tendency, the mean is most heavily influenced by any outliers or skewness. In a symmetrical distribution, the mean, median, and mode are all equal.

median

Partition values or fractiles such a quartile, a decile, etc. are the different sides of the same story. In other words, these are values that divide the same set of observations in different ways.

Empirical Relationship between Mean, Median and Mode In case of a moderately skewed distribution, the difference between mean and mode is almost equal to three times the difference between the mean and median. Thus, the empirical mean median mode relation is given as: Mean – Mode = 3 (Mean – Median)

Standard deviation – as the name suggests is a measure of the deviation. Deviation means change or distance. Hence standard deviation is a measure of change or the distance from a measure of central tendency – which is normally the mean. Hence, standard deviation is different from a measure of central tendency.

The measures of central tendency (mean, mode and median) are exactly the same in a normal distribution. The standard deviation is the average amount of variability in your data set. It tells you, on average, how far each score lies from the mean.

Standard Deviation Another measure of dispersion is standard deviation, which describes the typical difference (or deviation) between a data value and the mean. Outliers Measures of central tendency and dispersion can give misleading impressions of a data set if the set contains one or more outliers.

Advantages and disadvantages of measures of central tendency

• Good to use with ordinal data.
• It is generally unaffected by anomalies and so safer to use with extreme values.

The main goal of using measures of central tendency is to get an accurate description of the entire data. After all, when you calculate the mean, median or mode, you are looking at a value that represents the entire data.

The mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero. On the other hand, the one main disadvantage of the mean is its susceptibility to the influence of outliers.