Variability in Math

Introduction to variability in math:

In statistics math, variability or variation is nothing but the spread in a variable. Some of the common measures of variability in statistics math are range, variation, and standard deviation. In this article variability in math , we are going to discuss about finding the measures of variability through the example problems, which will be very useful for the math students.

Measures of Variability - Range:

Definition:

Range is the difference between a greater value and a smaller value.

Steps involved to learn range:

Step 1: Arrange the given numbers from ascending to descending order.

Step 2: Identify the larger value in the set of data

Step 3: Identify the smaller value in the set of data

Step 4: We have to find the difference between larger and smaller value.

Example problems:

Example 1:

Find the range for the following set of data:

{ 13 , 14 , 15 , 16 , 17 }

Solution:

Range   =  larger value - smaller value

=  17 - 13

=  4

Example 2:

Find the range for the following set of data:

{ 8 , 14 , 24 , 34 , 45 }

Solution:

Range   =  larger value - smaller value

=  45 - 8

=  37

Measures of Variability - Variance and Standard Deviation:

Definition:

Variance is the mean of the squared deviation from its expected value. The standard deviation is the square root of its variance.

Step-by-step explanation:

Step 1: Mean:Find the average or mean value of the given data

Step 2: Variance:To find the variance, get each difference from the mean value and square the each value and finally

average the result.

Step 3: Standard deviation: Find the square root of variance to calculate the standard deviation.

Example problem:

Find the variance and standard deviation for the given set of data:

{ 2, 9, 3, 1, 5 }

Solution:

Step 1: Mean

Mean   =  ` ( 2 + 9 + 3 + 1 + 5 ) / 5`

=  ` 20 / 5`

= 4

Step 2: Variance

Variance  =   `( (5-4)^2 + (9-4)^2 + (3-4)^2 + (1-4)^2 + (5-4)^2 )/5`

=   `( (1)^2 + (5)^2 + (-1)^2 + (-3)^2 + (1)^2 )/5`

=   `(1+25+1+9 + 1)/5`

=   `37/5`

=  7.4

Step 3:Standard deviation

Standard deviation  =  `sqrt ( 7.4 )`

=  2.72