The range is the difference between the greatest and least values in a set of data. For our exercise, the greatest value is 141 and the least value is 116.
Range: 141- 116=25
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= 126. Let's use this value and apply the formula to each value in the set.
x_n
x_n-x
(x_n-x)^2
141
141-126=15
15^2=225
116
116-126=- 10
(- 10)^2=100
117
117-126=- 9
(- 9)^2= 81
135
135-126=9
9^2=81
126
126-126=0
0^2=0
121
121-126=- 5
(-5 )^2=25
Sum of Values
512
Finally, since n= 6, we need to divide by 6 and then calculate the square root.
Standard Deviation: sqrt(512/6)≈ 9.24
