Pythagorist
Statistics

Mean, Median and Mode Calculator

Calculate the mean, median, mode, and range of any data set instantly. Enter your numbers separated by commas and get all four measures of central tendency with full step-by-step working.

Mean

5.285714

Median

5

Mode

7

Range

7

How it works

  1. Calculate the mean

    xˉ=4+7+2+9+5+7+37=377=5.285714\bar{x} = \frac{4 + 7 + 2 + 9 + 5 + 7 + 3}{7} = \frac{37}{7} = 5.285714

    Add all values together and divide by the count. Sum = 37, count = 7.

    Result:5.285714

  2. Sort the values (for median)

    2, 3, 4, 5, 7, 7, 92,\ 3,\ 4,\ 5,\ 7,\ 7,\ 9

    Arrange values in ascending order: 2, 3, 4, 5, 7, 7, 9.

  3. Find the median (middle value)

    median=5\text{median} = 5

    Odd count (7 values): the middle value is position 4 = 5.

    Result:5

  4. Find the mode (most frequent value)

    7 appears 2 times — more than any other value.

    Result:7

  5. Calculate the range

    range=9−2=7\text{range} = 9 - 2 = 7

    Range = largest − smallest = 9 − 2 = 7.

    Result:7

Mean, Median, Mode & Range

xˉ=∑xnrange=max−min\bar{x} = \frac{\sum x}{n} \qquad \text{range} = \text{max} - \text{min}
xˉx̄Mean (average)
∑x∑xSum of all values
nnNumber of values

Example substitution

xˉ=4+7+2+9+35=255=5\bar{x} = \frac{4 + 7 + 2 + 9 + 3}{5} = \frac{25}{5} = 5

For data set {4, 7, 2, 9, 3}: mean = 25 ÷ 5 = 5.

Worked examples

Find the mean, median, mode, and range of: 3, 7, 5, 3, 9, 5, 3.

  1. 1
    Mean: Sum = 35, count = 7. Mean = 35 ÷ 7 = 5
  2. 2
    Median: Sorted: 3, 3, 3, 5, 5, 7, 9. Middle value = 5
  3. 3
    Mode: 3 appears 3 times — most frequent. Mode = 3
  4. 4
    Range: 9 − 3 = 6
Answer: Mean = 5, Median = 5, Mode = 3, Range = 6

Find the median of: 12, 8, 15, 4, 20, 6.

  1. 1
    Sort the values: 4, 6, 8, 12, 15, 20
  2. 2
    Even count — find two middle values: Positions 3 and 4: 8 and 12
  3. 3
    Average the two middle values: (8 + 12) ÷ 2 = 10
Answer: Median = 10

Frequently asked questions

What is the mean?+

The mean is the sum of all values divided by the count. Also called the arithmetic average.

What is the median?+

The median is the middle value when data is ordered from smallest to largest. For an even count, average the two middle values.

What is the mode?+

The mode is the most frequently occurring value. A dataset can have more than one mode.

What is the range?+

The range is the difference between the largest and smallest values: max − min.

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