Question

You are a court administrator. There are presently 6 judges in the court system.         For October, you know the number of cases assigned to each judge. They are as follows:

5, 8 , 1, 3, 6, 7

Find the following:

1. Mean

2. Median

3. Standard Deviation

Answer 1

Solution:
Number of cases assigned to each judge are as follows:
5,8,1,3,6,7
Solution(a)
Mean can be calculated as
Mean = summation(X)/n = (5+8+1+3+6+7)/6 = 30/6 = 5
Solution(b)
Lets sort the data from smallest to largest value
1,3,5,6,7,8
Median can be calculated as
Median = (n+1)/2 = (6+1)/2 = 3.5th value
So median = (5+6)/2 = 5.5
Solution(c)
Standard deviation can be calculated as
Standard deviation = sqrt((Xi-mean)^2/(n-1)) = sqrt((1-5)^2 + (3-5)^2 + (5-5)^2 + (6-5)^2 +(7-5)^2 + (8-5)^2)/5) = sqrt((16+4+0+1+4+9)/5) = sqrt(34/5) = 2.61
So Mean = 5
Median = 5.5
Standard deviation = 2.61