Question

Melissa's birthday is next week and she has been receiving cards in the mail with different amounts of money. She has received five cards with the following amounts $10 $20 $25 $30 $40. If Melissa receives one more card in the mail with $25 will the standard deviation stay the same increase or decrease?

Answer 1

it wiki decrease because you added 25 more

Answer 2

Answer:

Hence, the standard deviation on adding one more card with $ 25 will decrease.

Step-by-step explanation:

             Amount in Cards      

                $ 10

                $ 20

                $ 25

                $ 30

                $ 40

Total        $ 125

( since 10+20+25+30+40=125 )

Now mean is the ratio of the total amount in all the cards to the total number of cards.

i.e. Mean=125/5=25

Hence, Mean=25

Now we calculate the standard deviation as:

Absolute Deviation        square of absolute deviation

|10-25|=15                                    225

|20-25|=5                                       25

|25-25|=0                                          0  

|30-25|=5                                        25

|40-25|=15                                     225  

Now we calculate the variance as:

$Variance=\dfrac{225+25+0+25+225}{5}\\\\\\Variance=\dfrac{500}{5}\\\\\\Variance=100$

Standard deviation is the square root of variation.

$Standard \ deviation=\sqrt{100}\\\\Standard\ deviation=10$

Hence, standard deviation=10

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Now when on more card is added that is we have a total of 6 cards.

Hence, Mean is calculated as:

$Mean=\dfrac{10+20+25+25+30+40}{6}\\\\\\Mean=\dfrac{150}{6}\\\\Mean=25$

Hence, Mean=25

Now we calculate the absolute deviation

Absolute deviation        Square of absolute deviation

|10-25|=15                                    225

|20-25|=5                                       25

|25-25|=0                                          0  

|25-25|=0                                          0

|30-25|=5                                         25

|40-25|=15                                      225  

Hence, variance is calculated as:

$Variance=\dfrac{225+25+0+25+225}{6}\\\\\\Variance=\dfrac{500}{6}\\\\\\Variance=83.33$

Standard deviation is the square root of variation.

So, as the variance decreases the standard deviation also decreases.

$Standard\ deviation=\sqrt{83.33}\\\\Standard\ deviation=9.1285$

Hence, standard deviation=9.1285

Hence, the standard deviation decreases on adding one more card.