Question

Suppose that you had the following data set. 100 200 250 275 300 Suppose that the value 250 was a typo, and it was suppose to be 260. How would the value of the standard deviation change?

Answer 1

Answer:

It will increase by  0.91180239

The corrrect standard deviation is 79.96874389

Explanation:

With the typo

u = (100 + 200 + 250 + 275 + 300)/ 5 = 225

1    100  - 225 =   -125

2   200  - 225 =   -25

3   250  - 225 =    25

4   275  - 225 =    50

5   300  - 225 =    75

s = √{(1/(N-1)  x  (-125)^2 + (-25)^2 + 25^2 + 50^2 + 75^2)}

s = √{1/4 x 25,000}

s = 79.0569415

With the correct value

u = (100 + 200 + 260 + 275 + 300)/ 5 = 227

1    100  - 227 =   -127

2   200  - 227 =   -27

3   260  - 227 =    33

4   275  - 227 =    48

5   300  - 227 =    73

s = √{(1/(N-1)  x  (-127)^2 + (-27)^2 + 33^2 + 48^2 + 73^2)}

s = √{1/4 x 25,580}

s = 79.96874389

Difference 0.91180239