The three averages
- Mean — add every value and divide by how many there are. The everyday "average".
- Median — sort the values and take the middle one. With an even count, average the two middle values.
- Mode — the value that appears most often. A dataset can have more than one mode, or none.
- Range — largest value minus smallest. A crude measure of spread.
Worked example
Data: 12, 15, 15, 18, 22, 25, 91
| Measure | Working | Result |
|---|---|---|
| Mean | 198 ÷ 7 | 28.3 |
| Median | middle of the sorted list | 18 |
| Mode | 15 appears twice | 15 |
| Range | 91 − 12 | 79 |
Notice the mean is 28.3, but six of the seven values are below 25. That single 91 pulls the mean far above where most of the data sits. The median of 18 describes this dataset far better.
Which average should you use?
| Situation | Best measure | Why |
|---|---|---|
| Exam marks, heights, symmetric data | Mean | Uses every value; no extreme outliers |
| Salaries, house prices, wealth | Median | A few very large values distort the mean |
| Shoe sizes, most common answer | Mode | Categories, not quantities |
| Data with obvious outliers | Median | Unaffected by extreme values |
Common mistakes
- Quoting the mean for skewed data such as income or property prices.
- Forgetting to sort before finding the median.
- Averaging the two middle values incorrectly when the count is even.
- Assuming every dataset has exactly one mode. It can have several, or none at all.
- Reporting an average without any measure of spread. Two datasets can share a mean and look nothing alike — see the standard deviation calculator.
Frequently Asked Questions
What is the difference between mean and median?
The mean adds all values and divides by the count. The median is the middle value once sorted. The median is more reliable when a few extreme values would distort the mean.
When should I use the median instead of the mean?
For skewed data such as salaries, house prices or wealth, where a small number of very large values pull the mean away from where most of the data sits.
Can a dataset have more than one mode?
Yes. Two modes make it bimodal, more make it multimodal, and if every value appears once there is no mode at all.
How do I find the median of an even number of values?
Sort them, take the two middle values and average them. For 4, 6, 8, 10 the median is 7.
What does range tell me?
The gap between the largest and smallest values. It is a quick measure of spread but very sensitive to a single outlier.
Why do average salary figures seem too high?
They are usually means, and a small number of very high earners pull the figure up. The median gives a more representative picture.
Weighted average
Jab har number ka wajan alag ho, saada average galat jawab deta hai.
Maan lijiye marks aise hain:
| Vishay | Marks | Credit | Marks × Credit |
|---|---|---|---|
| Maths | 85 | 4 | 340 |
| Physics | 70 | 3 | 210 |
| English | 90 | 2 | 180 |
| Kul | — | 9 | 730 |
Weighted average = 730 ÷ 9 = 81.1, jabki saada average 81.67 aata. CGPA isi tarah nikalti hai.
Outlier — ek number jo sab bigaad de
Outlier wo value hai jo baaki sabse bahut door ho. Mean use turant mehsoos karta hai, median lagbhag nahi.
Jaise: 20, 22, 21, 23, 19, 95
- Mean: 33.3 — koi bhi value iske aas-paas nahi
- Median: 21.5 — sacchai ke kareeb
Outlier dikhe to pehle dekhiye ki wo galti hai ya asli. Galti ho to hata dijiye; asli ho to use rakhiye lekin median bhi zaroor batayiye.
More questions
Weighted average kya hota hai?
Jab har value ka wajan alag ho, tab har value ko uske wajan se guna karke jod dete hain aur wajan ke kul se divide karte hain. CGPA isi tarah nikalti hai.
Outlier ka mean par kya asar padta hai?
Bahut zyada. Ek badi ya chhoti value poore mean ko kheench leti hai, jabki median lagbhag wahi rehta hai. Isi liye aise data mein median zyada sach batata hai.
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