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

It will increase by 0.91180239

The corrrect standard deviation is 79.96874389

Step-by-step 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