0.5 2.0 2.5 1.5 1.0 1.5
Let's find each statistic one at a time!
Range
The range is the difference between the greatest and least values in a set of data. For our exercise, the greatest value is 2.5 and the least value is 0.5.
Range: 2.5- 0.5=2
The mean of a data set is calculated by finding the sum of all values in the set and then dividing by the number of values in the set. In this case, there are 6 values in the set.
The standard deviation of a set of data is the average amount by which each individual value deviates or differs from the mean.
Standard Deviation
sqrt((x_1-x )^2 + (x_2-x )^2 + ... + (x_n-x )^2/n)
In the above formula, x_1, ... ,x_n are the values of the set of data, x is the mean, and n is the number of values. We have 6 values and the mean is x= 1.5. Let's use this value and apply the formula to each value in the set.
x_n
x_n-x
(x_n-x)^2
0.5
0.5-1.5=- 1
(- 1)^2=1
2
2-1.5=0.5
0.5^2=0.25
2.5
2.5-1.5=1
1^2= 1
1.5
1.5-1.5=0
0^2=0
1
1-1.5=- 0.5
(- 0.5)^2=0.25
1.5
1.5-1.5=0
0^2=0
Sum of Values
2.5
Finally, since n= 6, we need to divide by 6 and then calculate the square root.
Standard Deviation: sqrt(2.5/6)≈ 0.65
