Question

The standard deviation of the data:
5. 15. 25. 30. 35. 45, 55. lies between​

Answer 1

Numbers : 5 , 15 , 25 , 30 , 35 , 45 , 55

First , work out the average , or arithmetic mean of the numbers:

Count : 7 ( How many numbers )

Sum : 210 ( All the numbers added up )

Mean : 30 ( Arithmetic mean = Sum / Count )

Then, take each number, subtract the mean and square the result:

Differences: -25 , -15 , -5 , 0 , 5 , 15 , 25 ( Every Number minus Mean )

Differences: 625 , 225 , 25 , 0 , 25 , 225 , 625
( Square of each difference )

Now calculate the Variance :

Sum of Squared Differences :
1750
( Add up the Squared Differences )

Variance : 250
( Sum of Differences / Count )

Lastly, take the square root of the Variance:

Standard Deviation : 15.8113883
( The square root of the Variance )