8.2 , 10.1 , 2.6 , 4.8 , 2.4 , 5.6 , 7.0 , 3.3
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 10.1 and the least value is 2.4.
Range: 10.1- 2.4=7.7
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 8 values and the mean is x= 5.5. Let's use this value and apply the formula to each value in the set.
x_n
x_n-x
(x_n-x)^2
8.2
8.2-5.5=2.7
2.7^2=7.29
10.1
10.1-5.5=4.6
4.6^2= 21.16
2.6
2.6-5.5=- 2.9
(- 2.9)^2=8.41
4.8
4.8-5.5=0.7
0.7^2=0.49
2.4
2.4-5.5=- 3.1
(- 3.1)^2=9.61
5.6
5.6-5.5= 0.1
0.1^2=0.01
7.0
7.0-5.5=1.5
1.5^2=2.25
3.3
3.3-5.5=- 2.2
(- 2.2)^2=4.84
Sum of Values
54.06
Finally, since n= 8, we need to divide by 8 and then calculate the square root.
Standard Deviation: sqrt(54.06/8) ≈ 2.60
