standard deviation changes?

2017-11-12 11:51 pm

There are 15 numbers on a list, and the mean is 25. The smallest number on the list is changed from 12.9 to 1.29.

a. Is it possible to determine by how much the mean changes? If so, by how much does it change?

b. Is it possible to determine the value of the mean after the change? If so, what is the value?

c. Is it possible to determine by how much the median changes? If so, by how much does it change?

d. Is it possible to determine by how much the standard deviation changes? If so, by how much does it change?

I have problem with part d , i dont have the ans .

So , we need to compute the new ∑x and ∑(x^2 ) , the new ∑x = old ∑x + 1.29 -12.9

the new ∑(x^2 ) = old ∑(x^2 ) - (12.9^2) + (1.29^2) ...
However , the old ∑x and ∑(x^2 )are not provided , so we cant calculate the changes

回答 (1)

用戶65385

2017-11-12 11:59 pm

I'll do part of the answer:

The sum of the numbers is 15 x 25 = 375

Changing one number from 12.9 to 1.29

reduces that number by 11.61. So the new

sum of the numbers is 375 - 11.61 = 363.39,

and thus the new mean is 363.39 / 15 = 24.226

As for the median: since we're making the smallest

number even smaller, the median is unchanged - it's

still the 8th number, listed in size order.

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