Plany

Centrum nauki / Statystyka

Averages and spread: mean, median, mode, range and standard deviation

Three ways to describe a typical value, two ways to describe how spread out data is, and when to use each.

1 min czytaniaZaktualizowano 18 października 2026Autor: Sumzo teamSprawdził(a): Sumzo team

  • Mean: add the values and divide by how many there are.
  • Median: the middle value once the data is in order (the mean of the two middle values if the count is even).
  • Mode: the value that appears most often.
  • Range: largest value minus smallest value.

Rozwiązany przykład

Summarise 2, 4, 4, 4, 5, 5, 7, 9

Find the mean, median, mode and range of 2, 4, 4, 4, 5, 5, 7, 9.

Pokaż rozwiązanie
  1. There are 8 values adding to 40.
    xˉ=408=5\bar{x} = \frac{40}{8} = 5
  2. The middle two values are 4 and 5.
    median=4+52=4.5\text{median} = \frac{4 + 5}{2} = 4.5
  3. 4 appears most often; the range is 9 − 2.
    mode=4,range=7\text{mode} = 4,\quad \text{range} = 7

Odpowiedź: Mean 5, median 4.5, mode 4, range 7

Sprawdzone przez silnik matematyczny Sumzo

Standard deviation

The standard deviation measures how far values typically are from the mean. Square each distance from the mean, average those squares (the variance), then take the square root.

σ=∑(xi−μ)2n\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n}}
For a sample, divide by n − 1 instead of n.

Rozwiązany przykład

Standard deviation of the same data

Find the population standard deviation of 2, 4, 4, 4, 5, 5, 7, 9.

Pokaż rozwiązanie
  1. The squared distances from the mean 5 add up to 32.
    9+1+1+1+0+0+4+16=329 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32
  2. Divide by 8 for the variance, then take the square root.
    σ2=328=4,σ=2\sigma^2 = \frac{32}{8} = 4,\quad \sigma = 2

Odpowiedź: 2

Sprawdzone przez silnik matematyczny Sumzo

Kalkulatory

Ćwiczenia

Utknąłeś na zadaniu? Zapytaj Sumzo AI