Measures of Central Tendency Simplified

The Mean, Median and Mode are the measures of central tendency. Mean is the average of the values in the given data. Median is the middle term or value in the given data. Mode is the value that occurs most often or most number of times in the given data.

Definition of Mean Median and Mode
Arithmetic Mean can be defined as the sum of the values given in the data divided by the number of values.
Median can be defined as the middle value in a list of data arranged from the smallest to greatest.
Mode can be defined as the value which occurs most often in a given list.
Let us consider the data 6,7,9,6,8,4,3. The Mean of the given data would be (6+7+9+6+8+4+3)/7= 43/7 = 6.14. To find the median we need to arrange the given data in the ascending order and the middle value would be the median. 3,4,6,6,7,8,9. The middle value in the arranged list is 6 and hence the median is 6. Mode is the value that occurs the most number of times, 6 is such value and hence the mode.

To understand the Mean, Median and Mode of the given data let us consider a simple example problem. The responses of nine people as to how many times they visit a grocery store a month were, 8, 10, 9, 5, 8, 4,11, 8, 9.  Here let us first arrange the given data in the ascending order. 4, 5,8,8,8,9,9,10,11. Mean is the average of all the data values given, that would be[sum of the data values/total number of data values]. The sum of the data values is (4+5+8+8+8+9+9+10+11=72) the total number of data values is 9. So, the Mean = 72/9 = 8.  The middle value of an arranged data list is the Median. Here we have odd number of values and hence the middle value in the list, 8 is the median.
Mode is the value that occurs the most number of times in a list, 8 is the value which is occurring most number of times and hence the mode

What Does Mean Median and Mode Mean
Mean is sum of the data values divided by the number of data values. It is most useful when the data set has no outliers. Median is the middle value in a sorted list (If even numbered, 2 middle values-average them). It is most useful when the data set has outliers and there are no big gaps in the middle of the data. Mode is the data value(s) that occurs most often in a set of data. It is most useful when the data set has many identical values.