# Mean vs median vs mode: why “the average salary” is so often misleading

> A company of nine people announces an average salary of ₹11.5 lakh. Eight of them earn between ₹4 and ₹7 lakh. Nobody is lying; the word “average” is. This guide explains the mean, median and mode, shows how one big number bends the mean, and gives a simple rule for picking the right one.

Published 2026-10-08 by Toolcloak. 6 minute read. Original: https://toolcloak.pages.dev/articles/mean-vs-median-vs-mode-why-the-average-salary-is-misleading
Related free tool: [Statistics Calculator](https://toolcloak.pages.dev/tools/statistics-calculator)

Here is a job advertisement: “Our team of nine earns an average of ₹11.5 lakh a year.” It sounds great until you look at the payslips. Eight people earn between ₹4 and ₹7 lakh. The ninth, the founder, takes ₹60 lakh. The ad is technically true, and still misleading. The trick is that “average” can mean three different things, and they can disagree wildly.

> **In short**
> - **Mean** = add everything up and divide by the count. **Median** = the middle value when sorted. **Mode** = the value that appears most often.
> - In our example the mean is **₹11.5 lakh**, the median **₹5.5 lakh** and the mode **₹5 lakh**. The one big salary pulled only the mean.
> - When data is **skewed** or has **outliers** (incomes, house prices, response times), the **median** describes a typical person better.
> - Use the **mean** for fairly symmetric data and for totals, the **median** for typical values, and the **mode** for categories like shoe sizes.

## The three averages in one minute

All three try to answer the same question, “what is a typical value?”, in different ways. Take our nine salaries in lakh rupees per year: 4, 4.5, 5, 5, 5.5, 6, 6.5, 7 and 60.

**The nine salaries (₹ lakh a year)**

|  | Value |
| --- | --- |
| A | 4 L |
| B | 4.5 L |
| C | 5 L |
| D | 5 L |
| E | 5.5 L |
| F | 6 L |
| G | 6.5 L |
| H | 7 L |
| Founder | 60 L |

*Eight bars are close to each other. The ninth is almost ten times taller. The mean has to reflect all nine, so it is dragged toward the tall one.*

**Three answers to “what is typical?”**

|  | Value | Note |
| --- | --- | --- |
| Mean | ₹11.5 L | 103.5 ÷ 9. Every value counts, including the 60. |
| Median | ₹5.5 L | The 5th of 9 sorted values. Half earn more, half less. |
| Mode | ₹5 L | The most common value. Two people earn exactly 5. |

*The mean is more than double the median. A new hire expecting ₹11.5 lakh would be disappointed.*

## How to find each one

### Mean

Add up all the values and divide by how many there are. Here 4 + 4.5 + 5 + 5 + 5.5 + 6 + 6.5 + 7 + 60 = 103.5, and 103.5 ÷ 9 = 11.5. The mean uses every number, which is its strength (it is fair to all data) and its weakness (it is easily dragged around by one extreme number).

### Median

Sort the values and pick the middle one. With nine values the middle is the fifth, which is 5.5. If the count is even, there are two middle values, and you average them. For 3, 5, 7, 9 the median is (5 + 7) ÷ 2 = 6. The median ignores how large the extreme values are. It only cares about their position.

### Mode

The value that appears most often. In our data 5 appears twice and everything else once, so the mode is 5. A set can have no mode (all values different) or several. The mode is the only one of the three that works for categories: the most common shirt size, the most popular bus route.

**Finding the median step by step**

1. **Sort the numbers.** 4, 4.5, 5, 5, 5.5, 6, 6.5, 7, 60.
2. **Count them.** There are 9 values. The middle position is (9 + 1) ÷ 2 = 5.
3. **Read the 5th value.** It is 5.5. If the count were even, average the two middle ones.

Try it: [Statistics Calculator](https://toolcloak.pages.dev/tools/statistics-calculator). Paste a list of numbers to get the mean, median, mode, range and standard deviation at once.

## How one number bends the mean

Let us do an experiment. Keep the other eight salaries fixed and change only the ninth. As the top salary grows, the mean rises steadily. The median does not move at all, because the top person is still the top person and the middle is still the fifth value.

**Mean and median as the top salary grows (₹ lakh)**

| The ninth person’s salary (₹ lakh) | Mean | Median |
| --- | --- | --- |
| 10 | 5.9 | 5.5 |
| 20 | 7.1 | 5.5 |
| 40 | 9.3 | 5.5 |
| 60 | 11.5 | 5.5 |
| 100 | 15.9 | 5.5 |

*With a top salary of 10 the two are close (5.9 and 5.5). At 100, the mean is 15.9 and the median is still 5.5. This is why the median is called a robust measure.*

**From the median to the mean in our example (₹ lakh)**

| Step | Amount |
| --- | --- |
| Median | 5.5 |
| Pull of the founder | +6.0 |
| Mean | 11.5 |

*The gap between the two (6 lakh) is a quick signal that the data is lopsided. When the mean is far above the median, a few big values are at work.*

## Skew: when the three averages disagree

In a perfectly symmetric bell curve all three averages sit at the same point. In a **right-skewed** distribution, which has a long tail of big values, the order is usually mode, then median, then mean, from left to right. Incomes, house prices, hospital stays and the time to fix a bug all look like this. Few values are huge, and many are small to medium.

**A right-skewed distribution: the three averages in order**

| Value (arbitrary units) | How common each value is |
| --- | --- |
| 0 | 0 |
| 0.5 | 30.3 |
| 1 | 36.8 |
| 1.5 | 33.5 |
| 2 | 27.1 |
| 2.5 | 20.5 |
| 3 | 14.9 |
| 3.5 | 10.6 |
| 4 | 7.3 |
| 4.5 | 5 |
| 5 | 3.4 |
| 5.5 | 2.2 |
| 6 | 1.5 |

*Drawn from a standard gamma curve: mode 1, median about 1.68, mean 2. The long right tail pulls the mean furthest. If the mean is above the median, suspect a right skew.*

**Two honest sentences about the same data**

| “The average salary is ₹11.5 lakh” | “The typical salary is ₹5.5 lakh” |
| --- | --- |
| The mean | The median |
| True, and technically correct | Half the team earns more, half less |
| Raised by the founder’s ₹60 lakh | Not moved by the founder’s pay |
| Describes nobody in the room | Matches what a new hire will likely see |

*Whenever you read a headline with “average”, ask: mean or median?*

## Which one should you use?

**A simple guide to choosing**

| Box | What it means |
| --- | --- |
| Use the mean when… | The data is roughly symmetric, without wild outliers, and you care about totals. Example: average daily sales over a month to forecast the revenue. |
| Use the median when… | The data is skewed or has outliers, and you want a typical case. Examples: salaries, house prices, waiting times, delivery delays. |
| Use the mode when… | The data is in categories, or you want the most common choice. Examples: shirt sizes, most-used payment method, the busiest hour. |
| Show more than one when… | You are not sure. Giving mean and median together tells readers how lopsided the data is. |

*Good reports give two numbers, such as “median ₹5.5 lakh, mean ₹11.5 lakh”. The gap itself is information.*

## Other kinds of average you will meet

### The weighted mean

Sometimes values do not count equally. A course gives 20% to assignments, 30% to a midterm and 50% to the final. You scored 80, 60 and 70. The plain mean is (80 + 60 + 70) ÷ 3 = 70. The weighted mean is 0.2 × 80 + 0.3 × 60 + 0.5 × 70 = 16 + 18 + 35 = **69**. The final counts the most, so it pulls harder.

**Plain mean against weighted mean for the same three marks**

|  | Score |
| --- | --- |
| Assignments (20%) | 80 |
| Midterm (30%) | 60 |
| Final (50%) | 70 |
| Plain mean | 70 |
| Weighted mean | 69 |

*The weights decide the result. A grade calculator or the statistics tool above does this arithmetic for you.*

### The trimmed mean

Drop the highest and lowest values before averaging. Judges in diving and gymnastics do this to blunt a biased score. For our nine salaries, drop 4 and 60 and the mean of the remaining seven is 39.5 ÷ 7 ≈ **5.6 lakh**, very close to the median.

### The geometric mean

For growth rates you multiply rather than add, so the right average is the geometric mean. A fund that gains 50% one year and loses 50% the next has an arithmetic mean of 0%, but your money is down: 1.5 × 0.5 = 0.75. The true yearly rate is √0.75 − 1 ≈ −13.4%. The articles on [up 50 percent, down 50 percent](https://toolcloak.pages.dev/articles/up-50-percent-down-50-percent-and-you-are-not-back-to-zero) and [average return versus CAGR](https://toolcloak.pages.dev/articles/average-return-vs-cagr-why-20-percent-is-not-what-you-earned) walk through this trap.

## Five ways averages mislead

1. **The outlier hides in the mean.** One huge value shifts it. Always check the median.
2. **Two groups hiding in one.** If data has two clusters (say, junior and senior staff), no single average describes either group. Split it first.
3. **Averages of averages.** The mean of two city averages is not the national average unless the cities are the same size. Use a weighted mean.
4. **Percentages are not added.** Average the underlying counts, not the percentages.
5. **The mean of nothing.** The average family has 2.4 children, but no family does. The mean need not be a possible value, which is fine for planning and silly for describing.

> **A habit worth building:** When you see an average, ask three questions: which kind is it, how many values are behind it, and what is the spread? For the spread, see the [bell curve and standard deviation](https://toolcloak.pages.dev/articles/the-bell-curve-68-95-99-7-rule-z-scores-and-what-rare-really-means) guide.

## Quick practice

Five friends spend ₹200, ₹250, ₹300, ₹300 and ₹1,950 on a trip dinner. The mean is 3,000 ÷ 5 = ₹600, the median ₹300, and the mode ₹300. Which should the restaurant quote as the typical bill? The median, because one person ordered an expensive meal. Which should the group use to split the total fairly? Neither: the total of ₹3,000 is what matters, so the mean times five is the figure to split. The same data, two different questions, two different averages.

## Frequently asked questions

### What is the difference between mean, median and mode?

The mean is the sum divided by the count, the median is the middle value of the sorted list, and the mode is the most frequent value.

### Why is the median better for salaries?

A few very high salaries pull the mean up but do not change the middle value, so the median shows what a typical person earns.

### Can the mean be higher than every value except one?

Yes. With eight values near 5 and one value of 60, the mean is 11.5, which is above eight of the nine values.

### What if there are two middle values?

When the count is even, the median is the average of the two middle values. For 3, 5, 7, 9 it is 6.

### Can a data set have more than one mode?

Yes. If two values tie for the most frequent, the data is bimodal. If no value repeats, it has no mode.

### What is a weighted average?

An average in which some values count more than others, found by multiplying each value by its weight and adding. Grades often use it.