What is mean, median and mode?
In many statistical situations, like the distribution of weight, height, marks, profit, wages and so on, it has been noted that starting with rather low frequency, the class frequency gradually increases till it reaches its maximum somewhere near the central part of the distribution and after which the class frequency steadily falls to its minimum value towards the end. Thus, the central tendency may be defined as the tendency of a given set of observations to cluster around a single central or middle value and the single value that best represents the given set of observations is called the measure of central tendency. Mean, median and mode are all measures of central tendency.
Define mean, median and mode:
Mean: The average value of a set of data is called the mean. If x1,x2, x3, …. Xn are n values of a given variable then the mean value, represented by μ, would be sum of these x values divided by n.
Median: The middle value of a data set is called the median. It is represented by ‘Me’.
Mode: In a data set of various values of a variable, the number that occurs maximum number of times is called the mode. In other words the value with maximum frequency is called the mode.
How do you do mean median and mode?
Mean median and mode problems usually involve calculating mean median and mode. That can be done using the following formulas:
Mean = μ = [∑xi]/n
Median = Me = middle value obtained after arranging the values in ascending order.
Mode = Mo = the value that occurs most number of times or the value with maximum frequency.
Solved example: Find the mean, median and mode of the following numbers: 5, 4, 5, 5, 6, 7, 8, 9, 6, 8
Solution:
Mean = μ = [∑xi]/n = [5+4+5+5+6+7+8+9+6+8]/10 = 63/10 = 6.3
Median: Firs arrange the data in ascending order. So we have:
4, 5, 5, 5, 6, 6, 7, 8, 8, 9. The two middle numbers are 6 and 6. The average of these numbers is (6+6)/2 = 6. Therefore,
Me = 6
Mode: The number that occurs most number of times is 5. Therefore,
Mo = 5
