The measures of spread include the range, quartiles and the interquartile range, variance and standard deviation. Let's consider each one by one.
Interquartile Range:
Given the Data -> First Quartile = 2, Third Quartile = 5
Interquartile Range = 5 - 2 = 3
Range: 8 - 1 = 7
Variance:
We start by determining the mean,
[tex]\:1+\:2+\:3+\:3+\:3+\:5+\:8 / 7 = 3.57[/tex]
n = number of numbers in the set
Solving for the sum of squares is a long process, so I will skip over that portion and go right into solving for the variance.
[tex]\sum _{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n-1},\\\\=> SS/n - 1\\\\=> 31.714/7 - 1\\=> 5.28571[/tex]
5.3
Standard Deviation
We take the square root of the variance,
[tex]\sqrt{5.28571} = 2.29906[/tex]
2.3
If you are not familiar with variance and standard deviation, just leave it.
