Answer:
The standard deviation of the following data set is 32.2
Step-by-step explanation:
step 1
Find the mean
we have
[tex][56,78,123,34,67,9,20][/tex]
Sum the data and divided by the number of elements
[tex][56+78+123+34+67+91+20]/7=469/7=67[/tex]
step 2
For each number: subtract the Mean and square the result
[tex][(56-67)^{2},(78-67)^{2},(123-67)^{2},(34-67)^{2},(67-67)^{2},(91-67)^{2},(20-67)^{2}][/tex]
[tex][121,121,3,136,1,089,0,576,2,209][/tex]
step 3
Work out the mean of those squared differences
[tex][121+121+3,136+1,089+0+576+2,209]/7=1,036[/tex]
This value is called the "Variance"
step 4
Take the square root of the variance
[tex]standard\ deviation=\sqrt{1,036}=32.2[/tex]
