Hi readers! Today we will discuss about Central tendency Like Mean, Median & Mode. Central tendency helps us to find out the central value or average value of a statistical series of quantitative information.
Mean (average) = sum of the values/number of observations.
2 4 5 6 8 Mean = (2+4+5+6+8)/5= 25/5= 5.
Median– value of middle observation- after sorting the data in ascending order.
Example of odd number
2 3 4 7 9 Median value= 4.
10 21 31 40 52 67 70000 Median value= 40.
Example of even number
2 3 4 6 10 14 Even number of observations Median value= 5 = (4+6)/2.
When to use Median?
- Median is preferred when mean/average gets highly ‘distorted’ by few extreme values as in the data below (Mean = Sum/N = 3060/9 = 340, a poor measure of centre of the data).
Distribution of wealth is known to be highly distorted (skewed)- few individuals have high wealth, as in above data. Hence median is preferred over mean. Distribution of income and salary are also skewed, hence median income and median salary are preferred over mean income and mean salary.
- Median is used in 5-number summary and Boxplot
Mode– value of most frequently occurring observation in the data.
1 3 3 4 5 6 Mode value= 3
10 21 35 45 50 50 50 50 68 68 77 Mode value= 50
Some more example.
1 3 3 4 5 6 Unique modal value, 3.
1 2 2 3 4 5 5 6 Two modal values, 2 and 5.
1 2 3 4 5 6 No modal value.
Usage of Mode as a measure of central tendency is rare. It is mostly used in voting, i.e.- a candidate who secures largest number of votes is declared the winner
Suppose There are four candidate X, Y, Z & T and result has been declared after the elections. In this case candidate Y secures largest number of votes and is declared the winner. Hence The Mode here is Y.
Let us understand with one more example.Find out mean, median & mode of given below data set.
| 200 | 400 | 400 | 500 | 550 |
| 250 | 400 | 425 | 500 | 600 |
| 300 | 400 | 450 | 500 | 600 |
| 300 | 400 | 450 | 500 | 600 |
| 350 | 400 | 450 | 500 | 600 |
| 350 | 400 | 450 | 500 | 600 |
| 350 | 400 | 450 | 500 | 650 |
| 350 | 400 | 450 | 525 | 700 |
| 360 | 400 | 500 | 550 | 800 |
| 375 | 400 | 500 | 550 | 1000 |
