A measure of central tendency gives us an idea about where the middle of the data lies.
We shall discuss about the following in this post.
- Mean
- Median
- Mode
Mean
- It shall be used against discrete and continuous data
- This is equal to the sum of all values divided by the number of data
- Usually it is represented by x-bar x̄.
x̄ = Σx/n
Lets take the following example to explain mean. Here is the data about the length of the runways in commercial airports of Tamil Nadu.
| Airport | Runway length in meters |
| Chennai – I | 3,658 |
| Chennai – II | 2,925 |
| Trichy | 2,480 |
| Madurai | 2,285 |
| Coimbatore | 3,120 |
| Tuticorin | 1,351 |
| Salem | 1,806 |
Hence the mean length of runways
x̄ or μ = 3568+2925+2480+2285+3120+1351+1806 / 7 μ = 17,625/7 μ = 2518 meters!
You may use average function in Excel – =AVERAGE(D2:D8).
Median
When we sort the data in any order, the items found in the middle is called median.
Lets take the same example in ascending order.
| Airport | Runway length in meters | Average |
| Tuticorin | 1,351 | 2,518 |
| Salem | 1,806 | 2,518 |
| Madurai | 2,285 | 2,518 |
| Trichy | 2,480 | 2,518 |
| Chennai – II | 2,925 | 2,518 |
| Coimbatore | 3,120 | 2,518 |
| Chennai – I | 3,658 | 2,518 |
So 1351, 1806, 2285, 2480, 2925, 3120, 3658 we have 7 data. Lets take the data in the middle, which is 2480, which is our median.
If we have even number of samples, average of middle values is the median.
Excel function: =MEDIAN(D2:D8)
Mode
The observation data observed frequently in the population is called mode. Let’s modify the above given data slightly to explain mode.
| Airport | Runway length in meters |
| Tuticorin | 1,000 |
| Salem | 2,000 |
| Madurai | 2,000 |
| Trichy | 2,000 |
| Chennai – II | 3,000 |
| Coimbatore | 3,000 |
| Chennai – I | 4,000 |
2000 is repeated thrice. Hence this is the mode of this data set.
Excel function: =MODE.SNGL(E2:E8)
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