Question

Melissa’s birthday is next week and she has been receiving cards in the mail with different amounts of money. She has received 5 cards with the following amounts: $10, $20, $ 25, $30, $40. If Melissa receives one more card in the mail with $25, which of the following will happen?

Answer 1

a and b

Explanation:

its right

Answer 2

We have to choose an answer that best describes what will happen with the standard deviation. First we have to calculate the Mean without last $25. Mean 1= ( 10 + 20 + 25 + 30 + 40 ) / 5 = 25. Standard deviation: SD 1 = sqrt( ( 225 + 25 + 0 + 25 + 225 ) / 5 ) = sqrt ( 500/5 ) = sqrt ( 100 ) = 10. Then we have to calculcate the Mean with additional $25 : Mean 2 = ( 10 + 20 + 25 + 30 + 40 + 25 ) / 6 = 25 ( same again ). The new Standard Deviation: SD 2 = sqrt ( ( 225 + 25 + 0 + 25 +225 + 0 ) / 6 ) = sqrt( 500 / 6 ) = sqrt ( 83.33 9 = 9.13. 9.13 < 10. Answer: The standard deviation A ) Decreases.