Type your data and get the variance and standard deviation step by step: the mean, the squared differences and the final root. Plus the mean, median and mode.
Data
Separate them with commas and a space (3, 5, 7), semicolons or spaces. Decimals with a point: 2.5 3.1.
Examples:
Data read, sorted:3 · 5 · 7 · 7 · 9
Data (N)
5
Mean
6.2
Median
7
Mode
7
Range
6
Standard deviation
2√26/5 ≈ 2.04
Frequency table
xᵢ
fᵢ
Fᵢ
hᵢ
%
3
1
1
0.2
20 %
5
1
2
0.2
20 %
7
2
4
0.4
40 %
9
1
5
0.2
20 %
N
5
Mean (x̄)
Add up all the data: each value times how often it appears.
3 + 5 + 7·2 + 9 = 31
Divide by the number of data values, N = 5: x̄ = 31 / 5 = 6.2
Median (Me)
With the data sorted, the median is the middle value. There are N = 5 values, which is odd.
Middle position: (N + 1) / 2 = 3. Value number 3 is 7.
To find a position, look for the first row whose cumulative frequency (Fᵢ) reaches that number.
Me = 7
Mode (Mo)
The most repeated value is 7, 2 times: Mo = 7.
Range
Maximum − minimum = 9 − 3 = 6
Variance and standard deviation
How far the data are from the mean, on average. For each value: its distance to the mean, squared, times its frequency.