# اوسط، وسطانیہ اور منوال کا کیلکولیٹر

> اعداد کی فہرست کے لیے اوسط نکالیں: حسابی اوسط، میانہ، موڈ، حد، تعداد اور مجموعہ دیکھیں۔ مرتب اعداد میں درمیان کی قدریں نمایاں ہوتی ہیں۔

انٹرایکٹو صورت: https://www.calcopenly.com/ur/math/mean-median-mode-calculator
موضوع: ریاضی کے کیلکولیٹر

The mean is the sum of the values divided by how many there are. The median is the middle value once the data are sorted: the value at position (n + 1) ÷ 2 when n is odd, and the average of the two middle values when n is even. The mode is the value that occurs most often, and the range is the largest value minus the smallest.

For the 10 default quiz scores the sum is 849, so the mean is 84.9. Sorted, the 5th and 6th values are 85 and 88, which puts the median at 86.5; 92 appears three times and is the mode, and the range is 95 − 70 = 25.

Data can have several modes, all listed here, or none: when every value occurs equally often, no value is more typical than another. Standard deviation, quartiles and outliers are on the descriptive statistics calculator.

## اندراجات

- **Data**: Numbers separated by commas, spaces or new lines. The default is 10 quiz scores.

## نتائج

- Mean (average) — بنیادی نتیجہ
- Median
- Mode
- Range
- Count
- Sum
- Minimum
- Maximum
- Mean as a fraction

## فارمولا

$$
\bar x = \frac{1}{n}\sum_{i=1}^{n} x_i \qquad \tilde x = \begin{cases} x_{((n+1)/2)} & n \text{ odd} \\ \tfrac12\left(x_{(n/2)} + x_{(n/2+1)}\right) & n \text{ even} \end{cases}
$$

## حل شدہ مثالیں

### Quiz scores (default)

- Data: 85, 92, 78, 92, 88, 76, 95, 81, 92, 70
- **Mean (average): 84.9**
- **Median: 86.5**
- **Mode: 92 (appears 3 times)**
- **Range: 25**
- **Count: 10**
- **Sum: 849**
- **Minimum: 70**
- **Maximum: 95**
- **Mean as a fraction: 849/10 = 84 9/10**
- جانچ کا ماخذ: ⁨Python 3.8 statistics.mean = 84.9, statistics.median = 86.5, statistics.multimode = [92]; sum 849⁩

### calculator.net example, two modes

- Data: 10, 2, 38, 23, 38, 23, 21
- **Mean (average): 22.143**
- **Median: 23**
- **Mode: 23 and 38 (each appears twice)**
- **Range: 36**
- **Sum: 155**
- **Mean as a fraction: 155/7 = 22 1/7**
- جانچ کا ماخذ: ⁨calculator.net mean, median, mode, range calculator worked example: mean 22.143, median 23, modes 23 and 38, range 36⁩

### Calculator Soup example, 16 values

- Data: 9, 10, 12, 13, 13, 13, 15, 15, 16, 16, 18, 22, 23, 24, 24, 25
- **Mean (average): 16.75**
- **Median: 15.5**
- **Mode: 13 (appears 3 times)**
- **Range: 16**
- **Count: 16**
- **Sum: 268**
- **Minimum: 9**
- **Maximum: 25**
- جانچ کا ماخذ: ⁨Calculator Soup mean, median, mode calculator example output: mean 16.75, median 15.5, mode 13, range 16, count 16, sum 268⁩

### NIST StRD NumAcc1

- Data: 10000001, 10000003, 10000002
- **Mean (average): 10,000,002**
- **Median: 10,000,002**
- **Mode: No mode (every value appears once)**
- **Range: 2**
- **Mean as a fraction: لاگو نہیں**
- جانچ کا ماخذ: ⁨NIST StRD NumAcc1 certified mean 10000002; median and range by hand from the sorted values 10000001, 10000002, 10000003⁩

### Every value twice: no mode (edge case)

- Data: 1, 1, 2, 2
- **Mean (average): 1.5**
- **Median: 1.5**
- **Mode: No mode (every value appears twice)**
- **Range: 1**
- جانچ کا ماخذ: ⁨Calculator Soup convention: if all numbers occur the same number of times there is no mode; mean 6/4 and median (1 + 2)/2 by hand⁩

### Single value

- Data: -4.5
- **Mean (average): -4.5**
- **Median: -4.5**
- **Mode: −4.5 (appears once)**
- **Range: 0**
- **Count: 1**
- جانچ کا ماخذ: ⁨Definitions (NIST e-Handbook §1.3.5.1): with one value the mean, median and mode equal it and the range is 0⁩

## سوالات

### How do you find the mean, median and mode?

Add the values and divide by the count for the mean: 10, 2, 38, 23, 38, 23, 21 sum to 155, and 155 ÷ 7 = 22.14. Sort them (2, 10, 21, 23, 23, 38, 38) and take the middle one, the 4th, for the median: 23. Count repeats for the mode: 23 and 38 each appear twice, so both are modes. The range is 38 − 2 = 36.

### How do you find the median of an even number of values?

Sort the values and average the two in the middle, at positions n ÷ 2 and n ÷ 2 + 1. For the 16 values 9, 10, 12, 13, 13, 13, 15, 15, 16, 16, 18, 22, 23, 24, 24, 25, the 8th and 9th are 15 and 16, so the median is 15.5. This is the definition in the NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1.

### Can a data set have more than one mode or no mode?

Yes to both. NIST notes that the mode is not necessarily unique: 2, 3, 3, 5, 5, 8 has two modes, 3 and 5, and is called bimodal. When every value appears the same number of times, as in 4, 7, 9 or 1, 1, 2, 2, no value occurs more often than the others and the data have no mode.

### Which average should I use: mean, median or mode?

Use the mean for roughly symmetric data without extreme values, the median when a few values are far from the rest, and the mode for categories or the most common size. One outlier moves the mean but not the median: for 3, 4, 5 the mean and median are both 4, but changing 5 to 50 lifts the mean to 19 while the median stays 4.

### What is the difference between average and mean?

In everyday use "average" means the arithmetic mean, the sum divided by the count, and spreadsheet functions follow that: Excel's AVERAGE returns the mean. In statistics "average" is a looser word for any measure of center, so the median and mode are also called averages. When a report says "average" without saying which, it is almost always the mean.

### “⁨اوسط، وسطانیہ اور منوال کا کیلکولیٹر⁩” کتنا درست ہے؟

درستی آپ کی درج کردہ قدروں اور طریقے کے مفروضوں پر منحصر ہے۔ اعشاری حساب 50 بامعنی ہندسے استعمال کرتا ہے، مگر تخمینے، عددی طریقے اور ماخذ کا ڈیٹا کم درست ہو سکتے ہیں؛ دکھائی گئی قدروں کو راؤنڈ کرنے سے یہ حدود ختم نہیں ہوتیں۔ آزاد ذرائع کی حل شدہ مثالوں سے جانچ: 6۔ مثلاً، “⁨Quiz scores (default)⁩” کو ⁨Python 3.8 statistics.mean = 84.9, statistics.median = 86.5, statistics.multimode = [92]; sum 849⁩ سے جانچا جاتا ہے۔

### اس طریقے کا ماخذ کیا ہے؟

NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of location (mean, median, mode); NIST Statistical Reference Datasets: univariate summary statistics (NumAcc1); Python statistics module: mean, median, multimode.

## ماخذ

- [NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of location (mean, median, mode)](https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm)
- [NIST Statistical Reference Datasets: univariate summary statistics (NumAcc1)](https://www.itl.nist.gov/div898/strd/univ/homepage.html)
- [Python statistics module: mean, median, multimode](https://docs.python.org/3/library/statistics.html)