Explain the various measure of central tendency?

In statistics, the general level, characteristic, or typical value that is representative of the majority of cases. Among several accepted measures of central tendency employed in data reduction, the most common are

·   The arithmetic mean (simple average)

·   The median

·   The mode.

FOR EXAMPLE, one measure of central tendency of a group of high school students is the average (mean) age of the students.

Central tendency is a term used in some fields of empirical research to refer to what statisticians sometimes call "location". A "measure of central tendency" is either a location parameter or a statistic used to estimate a location parameter.

Examples include:-

·   Arithmetic mean, the sum of all data divided by the number of observations in the data set.

·   Median, the value that separates the higher half from the lower half of the data set.

·   Mode, the most frequent value in the data set.

Measures of central tendency, or "location", attempt to quantify what we mean when we think of as the "typical" or "average" score in a data set.

The concept is extremely important and we encounter it frequently in daily life. For example, we often want to know before purchasing a car its average distance per litre of petrol. Or before accepting a job, you might want to know what a typical salary is for people in that position so you will know whether or not you are going to be paid what you are worth. Or, if you are a smoker, you might often think about how many cigarettes you smoke "on average" per day. Statistics geared toward measuring central tendency all focus on this concept of "typical" or "average."

As we will see, we often ask questions in psychological science revolving around how groups differ from each other "on average". Answers to such a question tell us a lot about the phenomenon or process we are studying

Arithmetic Mean:

the sum of the numbers divided by the number of values, often called the ”Average”

·   Add all values together

·   Divide by the number of values to obtain the mean.

Example:

The Mean of 07, 12, 24, 20, 19 is:

(07+12+24+20+19)/05 = 16.4

Median:

·   The value which divides the values into two equal halves, which half of the values being lower than the median and half higher than the median

·   Short the values in to ascending order.

·   If you have an odd number of values, the median is the middle value.

·   If you have an even number of values, the median is the arithmetic mean of the two middle values.

Example:

The median of the above series is:

In Ordinary form:  07, 12, 24, 20, 19

In Ascending order: 07, 12, 19, 20, 24

Median is 19

Mode:

The most frequently occurring value (or Values)

·   Calculate the frequencies for all of the values in the data

·   The mode is the value (or values) with the highest frequency.

Example:

For individuals having the following ages:

18, 18, 19, 20, 20, 20, 21 and 23

The mode is 20 (most frequently occurring value)