Mathematical ‘MEAN’ means Average it can be a small data like average of marks of students in a class or it can be large data like the average height of Chinese adult male population, so mathematics has developed methods to handle all this and I shall show you how. But at the same time many students generally jump up and want to find out what is MEDIAN and MODE? Is that not the average?
So let us start with some very simple definitions.
Mean: It can be defined as the sum total of all the observations divided by the number of observations. ( Note :- the observations have to be quantitative and not qualitative)
Median: If the data is arranged in the increasing or decreasing order then the middlemost value of the data is known as the median.
Mode: If the data is given a glance then also we can get to know one very important property of it that is which observation has appeared the maximum number of times.
This reminds me of a very important property of mode that is if I say “Jeans are in fashion” that is literal statement but If I say “Of all the clothes jeans is the mode” then it will be a mathematical statement but I am actually talking about the same thing.
Range: If the data is arranged in increasing or decreasing order then the difference between the highest value and the lowest value of data is called the range.
In order to understand these concepts I shall take the help of data that I have from a Horse Racing Track.
This data has the age, height, weight, color and sex of the horses.The age, height and weight are quantities therefore mean can be very easily found for them. However color and sex are qualitative and hence their data will not lend itself for finding the mean.
Thus while doing analysis with this data we shall keep the above mentioned things in mind
Data of Horses who ran 64 races against each other in the year 2004-05
S.No | Name Of The Horse | Height (Hands) |
Weight | Age | Sex | color | No. Of Races Won Out Of 64 |
1 | Kojari | 17 | 420 | 4 | Gelding | Bay | 9 |
2 | Radience | 15.4 | 424 | 5 | Filly | Bay | 3 |
3 | Dare to Dream | 15.1 | 614 | 9 | Filly | Chestnut | 0 |
4 | Resoning | 15.2 | 430 | 4 | Filly | Chestnut | 2 |
5 | Power Zane | 15.7 | 415 | 4 | Gelding | Grey | 4 |
6 | Flaming Bay | 15.4 | 434 | 6 | Filly | Bay | 2 |
7 | Classical Act | 15.6 | 500 | 4 | Gelding | DKB | 3 |
8 | Zurbaran | 15.7 | 510 | 5 | Gelding | Bay | 4 |
9 | Exuberant | 15.8 | 514 | 4 | Gelding | Grey | 4 |
10 | Silver Line | 14.11 | 516 | 7 | Gelding | Grey | 1 |
11 | Grand Finale | 15 | 414 | 5 | Mare | Bay | 2 |
12 | Litoleur Glamour | 15 | 620 | 6 | Mare | Grey | 0 |
13 | Frantic | 15.2 | 540 | 4 | Filly | Chestnut | 1 |
14 | Free Radical | 15.5 | 500 | 3 | Gelding | Chestnut | 2 |
15 | Rapidash | 16 | 416 | 4 | Filly | Dark Brown | 10 |
16 | Glory Of Dancer | 15 | 590 | 8 | Horse | Bay | 0 |
17 | Hymn | 15.3 | 420 | 5 | Horse | Bay | 3 |
18 | Bold Cruizer | 15.2 | 570 | 7 | Horse | Grey | 2 |
19 | Cancordial | 15.1 | 420 | 3 | Gelding | Chestnut | 7 |
20 | Crwacan | 15.1 | 460 | 3 | Gelding | Chestnut | 5 |
So from the data table if I have to find the average of height, weight and age I shall do the following
Sum of heights of all the horses = 307.41
Mean height = 307.41 / 20 =15.37 hands (as the height of horses is measured in hands)
For weight also we follow the same technique
Sum of all the weights of horses = 9727 kg
So the mean weight will be = 9727 / 20 = 486.35 kg
Similarly for age also we can see the mean is = 5 years
But I cannot apply the same rule for finding the mean of color and sex since these are qualitative data hence they do not lend themselves for the inspection of mean
Similarly if we write the heights of all the horses in increasing order then the average of the heights of the two middlemost horses (that is the 10^{th} and the11th horse) shall give us the median height.
While if we see the color of the horses and find that 7 out of 20 have Bay color which is of maximum frequency this means that the mode is Bay
(Note :- mean can work for numeric data like age but mean shall not be a good estimate of the average color)
For finding the range of the heights we get the maximum height (17) and the minimum height (14.11). Then we find the difference between the two (17 - 14.11) which gives us the range (2.89 hands)