Question

I need help with this. Both Standard Deviation and the Mean. Both have answer choices of Decrease, Increase, or stay the same.

Answer 1

The mean will stay the same.

The standard deviation will decrease.

Explanation:

For the 5 cards, she has received, the mean will be:

μ=(∑x)/n

=125/5

=25

The mean is 25 and the standard deviation is 10.

σ=10

If a new card is received with $25, then the sum will be $150

So the new mean will be:

μ'=(∑x)/n

=150/6

=25

And the new standard deviation will be:

σ'= 9.12

We can clearly see that

μ= μ'

and

σ> σ'

So the mean will remain the same and standard deviation will decrease. .