Question

Find the standard deviation of the following data set: 9, 12, 15, 9, 45, 6. Round to the nearest hundredth if needed.

Answer 1

13.27

Explanation:

1. Find the mean (average):

(sum of data set)/(count of data)

9+12+15+9+45+6=96

96/6=16

2. For each data point, find the square of the distance to the mean. Remember to take the absolute value of the distance.

9-16=-7 absolute value: 7 squared:49

12-16=-4 absolute value: 4 squared: 16

15-16=-1 absolute value: 1 squared: 1

45-16= 29 absolute value: 29 squared: 841

6-16=-10 absolute value: 10 squared: 100

3. Take the sum of the number from step 2.

49+16+1+49+841+100=1056

4. Divide the sum by the count of data points.

1056/6=176

5. Take the square root.

`√(176) =13.266499161422`

Round the number to the nearest hundredth to get 13.27.