Mean, Median and Mode: How to Find Them with Examples

Mean, median and mode are the three main ways to describe the "centre" of a set of numbers – from exam marks and cricket scores to salaries and house prices. This guide explains how to find the mean, median and mode with the formulas and solved examples, shows when each one is the best choice, and covers the range, the weighted average and standard deviation.

What Is an Average?

An average is a single number that represents a whole set of data. In everyday speech "average" usually means the mean, but statisticians use three measures of central tendency – mean, median and mode – because each tells a slightly different story about the data.

How to Find the Mean

The mean (arithmetic mean) is what most people call the average:

Mean = Sum of all values ÷ Number of values

Example: a batter scores 4, 8, 6, 5, 3, 8 and 9 runs in seven matches.

1. Sum: 4 + 8 + 6 + 5 + 3 + 8 + 9 = 43
2. Number of values: 7
3. Mean = 43 ÷ 7 ≈ 6.14 runs

How to Find the Median

The median is the middle value when the data is arranged in order.

Odd number of values

Sort the scores above: 3, 4, 5, 6, 8, 8, 9. With 7 values the middle one is the 4th, so the median is 6.

Even number of values

For 12, 15, 11, 18, sort them: 11, 12, 15, 18. The two middle values are 12 and 15, so the median is (12 + 15) ÷ 2 = 13.5.

A general rule: the median is at position (n + 1) ÷ 2 in the sorted list.

How to Find the Mode

The mode is the value that appears most often. In 3, 4, 5, 6, 8, 8, 9 the mode is 8. A data set can have:

• No mode – every value appears once (1, 2, 3, 4).
• One mode – unimodal (2, 3, 3, 5).
• Two or more modes – bimodal or multimodal (2, 2, 5, 7, 7).

The mode is the only average that works for non-numerical data, such as the most common shoe size or favourite colour in a class.

Range: How Spread Out Is the Data?

Range = Highest value − Lowest value

For the batter's scores, the range is 9 − 3 = 6 runs. The range is quick to calculate but is affected by a single extreme value, so statisticians also use the interquartile range and standard deviation.

Mean vs Median vs Mode: Which Should You Use?

The mean uses every value, but one very large or very small value – an outlier – can pull it a long way. Consider five monthly salaries: ₹25,000, ₹28,000, ₹30,000, ₹32,000 and ₹5,00,000.

• Mean = ₹6,15,000 ÷ 5 = ₹1,23,000 – higher than four of the five salaries.
• Median = ₹30,000 – a much better picture of a "typical" salary.

This is why reports on incomes and property prices usually quote the median.

Weighted Average

When some values count more than others, use a weighted average:

Weighted mean = Σ(value × weight) ÷ Σ(weights)

Example: a student scores 80 in a 4-credit subject, 70 in a 3-credit subject and 90 in a 2-credit subject. Weighted average = (80×4 + 70×3 + 90×2) ÷ (4 + 3 + 2) = (320 + 210 + 180) ÷ 9 = 710 ÷ 9 ≈ 78.9. A simple mean of the three marks would give 80, which overstates the result because the lowest mark carried more credits. The same method calculates CGPA, average purchase prices of shares and grade point averages.

Standard Deviation in Brief

Standard deviation measures how far values typically are from the mean. A small standard deviation means the values are clustered close together; a large one means they are spread out. For the data 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5 and the population standard deviation is exactly 2. Our average calculator shows the standard deviation along with the other measures.

Mean of Grouped Data

For data given in a frequency table, multiply each value (or class mid-point) by its frequency, add these products, and divide by the total frequency. If 5 students scored 10, 8 scored 15 and 7 scored 20, the mean is (50 + 120 + 140) ÷ 20 = 310 ÷ 20 = 15.5. The same idea extends to class intervals in school statistics, using the mid-point of each interval.

Mean, Median and Mode in Excel

• Mean: =AVERAGE(A2:A20)
• Median: =MEDIAN(A2:A20)
• Mode: =MODE.SNGL(A2:A20), or =MODE.MULT for several modes
• Range: =MAX(A2:A20)-MIN(A2:A20)
• Weighted average: =SUMPRODUCT(A2:A4,B2:B4)/SUM(B2:B4)
• Standard deviation: =STDEV.P (population) or =STDEV.S (sample)

Where You Use Averages in Real Life

• Exams: class average marks, percentiles and CGPA.
• Sport: batting and bowling averages, run rates.
• Money: average monthly spending, average share purchase price, median salaries.
• Health: average daily steps, blood sugar readings.
• Business: average order value, most popular product (mode).

Practice Problem with Solution

A class test has these marks out of 20: 12, 15, 18, 15, 9, 14, 15, 20, 11, 16.

• Mean: sum = 145, n = 10, so mean = 14.5.
• Median: sorted 9, 11, 12, 14, 15, 15, 15, 16, 18, 20; the middle two are 15 and 15, so median = 15.
• Mode: 15 appears three times, so mode = 15.
• Range: 20 − 9 = 11.

The mean is slightly below the median because the low score of 9 pulls it down – a small example of how outliers affect the mean more than the median.

Finding a Missing Value from the Mean

If you know the mean and all but one value, you can find the missing one. Example: the mean of five numbers is 12. Four of them are 10, 14, 9 and 15. Total needed = 12 × 5 = 60. The four known values add up to 48, so the missing number is 60 − 48 = 12. The same method tells you what score you need in a final test to reach a target average.

Skewness: When Mean and Median Differ

If the mean is greater than the median, the data is usually right-skewed – a few very large values stretch the upper end, as with incomes. If the mean is less than the median, the data is left-skewed, with a few very small values, as with an easy test where most students score highly but a few score very low. Comparing the two is a quick way to spot skew without drawing a graph.

Quick Tip

When someone quotes an "average", ask which one. A company's "average salary" or a city's "average house price" can look very different depending on whether it is the mean or the median.

Frequently Asked Questions

Note: Examples are rounded to two decimal places where needed.