Mean, Median, Mode Calculator

Calculate the mean (average), median (middle value), and mode (most common) of a data set. Includes frequency distribution and range analysis.

Central Tendency

Mean (Average)

6.2000

sum ÷ count

Median (Middle)

6.5000

position 5

Mode

8

Unimodal

Count10
Sum62.00
Range8.00

Enter Your Data

Parsed 10 numbers

Summary Statistics

6.20

Mean

6.50

Median

8

Mode

8.00

Range

Sorted Data

2
4
4
5
6
7
8
8
8
10
Median positionMode value(s)

Frequency Distribution

Purple bars indicate the mode(s).

How It's Calculated

Mean (Average)

Mean = Sum ÷ Count = 62.00 ÷ 10 = 6.2000

Median (Middle Value)

With 10 values (even), the median is the average of positions 5 and 6

Median = 6.5000

Mode (Most Frequent)

8 appears 3 times
Mode = 8

Range

Range = Max - Min = 10 - 2 = 8.00

Frequency Table

ValueFrequencyRelative (%)Cumulative (%)
2110.0%10.0%
4220.0%30.0%
5110.0%40.0%
6110.0%50.0%
7110.0%60.0%
8330.0%90.0%
10110.0%100.0%

?How Do You Calculate Mean, Median, and Mode?

Mean = sum of all values divided by count. Median = middle value when sorted (or average of two middle values if even count). Mode = most frequently occurring value. For data [3,5,5,7,9]: Mean = (3+5+5+7+9)/5 = 5.8. Median = 5 (middle value). Mode = 5 (appears twice). A data set can have no mode, one mode (unimodal), or multiple modes (bimodal/multimodal).

What Are Mean, Median, and Mode?

Mean, median, and mode are the three main measures of central tendency in statistics. Mean is the average of all values, median is the middle value when sorted, and mode is the most frequently occurring value.

Key Facts About Mean, Median, and Mode

  • Mean formula: sum of values / count of values
  • Median: sort data, find middle value (or average of two middle if even count)
  • Mode: value that appears most frequently (can have multiple modes)
  • Mean is affected by outliers; median is not
  • A data set can have no mode if all values appear equally
  • Bimodal data has two modes; multimodal has more than two
  • In a normal distribution, mean = median = mode
  • Skewed data: mean pulls toward the tail, median stays central

Quick Answer

Mean = sum of all values divided by count. Median = middle value when sorted (or average of two middle values if even count). Mode = most frequently occurring value. For data [3,5,5,7,9]: Mean = (3+5+5+7+9)/5 = 5.8. Median = 5 (middle value). Mode = 5 (appears twice). A data set can have no mode, one mode (unimodal), or multiple modes (bimodal/multimodal).

Frequently Asked Questions

The mean (average) is the sum of all values divided by the number of values. For example, the mean of 2, 4, 6 is (2+4+6)/3 = 4. The mean is sensitive to outliers - extreme values can significantly affect it.
The median is the middle value when numbers are sorted. For odd counts, it's the exact middle. For even counts, it's the average of the two middle values. The median is resistant to outliers, making it useful for skewed data.
The mode is the most frequently occurring value. A dataset can have no mode (all values unique), one mode (unimodal), or multiple modes (multimodal). For example, in 1,2,2,3,3, both 2 and 3 are modes.
Use the mean for symmetric data without outliers. Use the median when data is skewed or has outliers (like income, house prices). For example, median household income is preferred because a few billionaires would skew the mean.
The range is the difference between the maximum and minimum values. It gives a simple measure of spread but is sensitive to outliers. For a more robust measure of spread, consider interquartile range or standard deviation.

Last updated: 2025-01-15