standard deviation

Question

Find the standard deviation of the data set. Round your answer to the nearest tenth.

12, 14, 15, 17, 19, 22, 23

Answer 1

The formula for Sample Standard Deviation:

The mean ( x ) =   (12+ 14+ 15+ 17+ 19+ 22+ 23)/7

= 122/7

= 17.42

Then for each number: subtract the Mean and square the result

(12 - 17.42)² = (- 5.42)² = 29.37

(14 - 17.42)² = (-3.42)² = 11.69

(15 - 17.42)² = (-2.42)² = 5.85

(17 - 17.42)² = (-0.42)² = 0.17

(19 - 17.42)² = (1.58)² = 2.49

(22 - 17.42)² = (4.58)² = 20.67

(23 - 17.42)² = (5.58)² = 31.13

add up all the values

Sum (N) = 29.37 + 11.69 + 5.85 + 0.17 + 2.49 + 20.67 + 31.13

                              = 49.6

Subtract by 1 then form of N - 1

N - 1 = 49.6 - 1

                  = 48.6

1 is Divide by N - 1 then the form of 1/(N-1)

1/(N-1) = 1/48.6 = 0.0205

√1/(N-1)∑(x₁ - x ) = √0.0205(12 - 17.42)

                                                                    = √0.0205(-5.42)

                                                                    = √ - 0.11111

 Then the solution of Sample Standard Deviation = √ - 0.11111.

Comments

Sum = 29.37 + 11.69 + 5.85 + 0.17 + 2.49 + 20.67 + 31.13 = 49.6.

Standard deviation = √(49.6/7) = √7.0857 = 2.662 = 2.7.

Therefore, standard deviation is 2.7.