In this article
A small company advertises an average monthly salary of ₹70,000. A job seeker hears that, imagines a comfortable middle, and applies. Then the offer comes in at ₹30,000 and everyone on the team earns about the same. Nobody lied. The word “average” just hid which average was used.
There are three common averages, and they answer three different questions. Picking the right one is the difference between a number that describes the group and a number that only sounds good.
The three averages in one example
Take seven people at that company. Six are employees. One is the owner, who also pays himself through the same payroll. Monthly pay in thousands of rupees:
| Person | Monthly pay |
|---|---|
| Employee 1 | ₹25,000 |
| Employee 2 | ₹28,000 |
| Employee 3 | ₹30,000 |
| Employee 4 | ₹32,000 |
| Employee 5 | ₹35,000 |
| Employee 6 | ₹38,000 |
| Owner | ₹3,00,000 |
Total payroll is ₹4,88,000 across seven people.
The mean is more than double what six of the seven people earn. The median stays with the typical person.
- Mean: add everything up and divide by how many there are. Every value counts, so one huge value pulls it up.
- Median: sort the list and take the middle one (for an even count, the mean of the two middle ones). It ignores how far the extremes are.
- Mode: the value that appears most often. It is the only one that works for categories, like the most common shoe size.
Why one number can move the mean so much
Remove the owner and the mean drops to ₹31,333. One person moved the “average” by more than ₹38,000. Now add an eighth employee earning ₹40,000: the mean becomes ₹66,000, the median becomes ₹33,500.
The median barely moved when the group changed. The mean swung by tens of thousands.
Which one to use
| Question | Best average | Why |
|---|---|---|
| What does a typical person earn? | Median | Not distorted by a few very high or low values |
| What will this cost in total, per head? | Mean | You need the total divided fairly, extremes included |
| Which size should the shop stock most? | Mode | It is the most common value |
| Marks in a class with no extreme scores | Mean | Values are balanced and every score matters |
Mean for totals, median for typical, mode for most common.
Shoe sizes make the mode concrete. A shop sold sizes 6, 7, 7, 7, 8, 8, 9, 10 and 11 in a day. The mean is 8.1, the median is 8 and the mode is 7. A shop that stocks 8.1 can’t exist. A shop that stocks more 7s sells more shoes.
The average-speed trap
You drive 120 km to a city at 60 km/h and come back at 40 km/h. The average of 60 and 40 is 50, but your average speed for the trip is not 50. The way out is to ask for total distance over total time.
- 1Time going120 km ÷ 60 km/h = 2 hours.
- 2Time returning120 km ÷ 40 km/h = 3 hours.
- 3Total distance over total time240 km ÷ 5 hours = 48 km/h.
You spent more time at the slower speed, so it counts for more. The same logic shows up with percentages: averaging growth rates directly gives the wrong answer, which the story of a 50% rise followed by a 50% fall shows.
Questions people ask
What is the difference between mean, median and mode?
The mean is the sum divided by the count. The median is the middle value when the numbers are sorted. The mode is the value that appears most often.
Which average is best for salaries?
The median, because a few very high salaries inflate the mean. In the example above the mean is ₹69,714 while six of seven people earn ₹38,000 or less.
Can there be more than one mode, or none?
Yes. If two values tie for most common there are two modes. If every value appears once there is no mode.
How do I find the median of an even number of values?
Sort the list and take the mean of the two middle values. For 25, 28, 30, 32, 35, 38, 40 and 300, the middle two are 32 and 35, so the median is 33.5.
Why is the average speed of 60 and 40 km/h not 50?
Because you spend more time at the slower speed. Use total distance divided by total time: 240 km over 5 hours is 48 km/h.