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?

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. The standard deviation A ) Decreases.