subject: Range Variance [print this page] Introduction to range variance: Introduction to range variance:
In general, Range means the value we obtained as a result of difference between a greater value and a smaller value.
The variance of a random variable or distribution is the expectation, or mean, of the deviation squared of that variable from its expected value or mean. ( Source - Wikipedia )
In this article of range variance, we are going to discuss about range and variance of the data set.
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Range of a Data Set:
Steps involved to find range:
Step 1: First arrange the numbers from ascending order to descending order.
Step 2: Identify the larger value in the given data
Step 3: Identify the smaller value in the given data
Step 4: Find the difference between larger and smaller value.
Example problems:
Example 1:
Find the range for the following data set:
{ 45 , 15 , 16 , 25 , 10 }
Solution:
Range = larger value - smaller value
= 45 - 10
= 35
Example 2:
Find the range for the following data set:
{ 21 , 30 , 19 , 32 , 36 }
Solution:
Range = larger value - smaller value
= 36 - 19
= 17
Practice problems:
1) Find the range for the following data set:
{ 23 , 15 , 20 , 31 , 44 }
2) Find the range for the following data set:
{ 10 , 56, 29, 56 , 34}
Answer key:
1) 29 2) 46
Variance of a Data Set:
Steps involved to find Variance:
Step 1: Mean:Find the average or mean value of the given set of data.
Step 2: Variance:To find the variance, get each difference from the mean value and square the each value and finally
