Question

What is the standard deviation of the following data set rounded to the nearest tenth? 56 ,78 ,123 , 34, 67, 91, 20

Answer 1

C. 32.2

Explanation:

Answer 2

The standard deviation of the following data set is 32.2

Explanation:

step 1

Find the mean

we have

`[56,78,123,34,67,9,20]`

Sum the data and divided by the number of elements

`[56+78+123+34+67+91+20]/7=469/7=67`

step 2

For each number: subtract the Mean and square the result

`[(56-67)^(2),(78-67)^(2),(123-67)^(2),(34-67)^(2),(67-67)^(2),(91-67)^(2),(20-67)^(2)]`

`[121,121,3,136,1,089,0,576,2,209]`

step 3

Work out the mean of those squared differences

`[121+121+3,136+1,089+0+576+2,209]/7=1,036`

This value is called the "Variance"

step 4

Take the square root of the variance

`standard\ deviation=√(1,036)=32.2`