Solves Variance of a Dataset

Enter dataset, separated by a comma

\sigma^2=\frac{\sum_{ }^{ }\left(x-\overline{x}\right)^2}{n-1}

Variance measures how spread out the numbers in a data set are from the average. It tells us how much the numbers differ from the mean.

Let’s say we have a list of numbers: 2, 4, 6, 8, 10

Step 1: Calculate the mean (average) of the numbers: (2 + 4 + 6 + 8 + 10) / 5 = 6

Step 2: Calculate the difference between each number and the mean:

2 – 6 = -4

4 – 6 = -2

6 – 6 = 0

8 – 6 = 2

10 – 6 = 4

Step 3: Square each difference:

(-4)^2=16, \\ (-2)^2=4, \\ (-0)^2=0, \\ (2)^2=4, \\ (4)^2=16

Step 4: Calculate the average of the squared differences:

\frac{16+4+0+4+16}{5} = 8- Imagine you have a group of friends who all have different ages. The variance tells us how spread out their ages are from the average age.
- If they are all close to the same age, the variance is small.
- If they are all different ages, the variance is larger.

Mixed numbers, proper fractions, improper fractions, fraction addition, fraction subtraction, and more...

Convert decimal to fraction, significant figures, decimal places, adding and subtracting decimal,...

Percentage error, changes, quantity, percentage conversions and more worksheets...

Ratio, direct proportion, inverse proportion, Hooke’s law, Charles’s and Ohm’s law

Laws of indices, power, roots, square roots, equation with indices, indexes...

Brackets, order of precedence, division, multiplication and...( watch math tutorials )