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
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
