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

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

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=(225+25+0+25+225)/(5)\\\\\\Variance=(500)/(5)\\\\\\Variance=100`

Standard deviation is the square root of variation.

`Standard \ deviation=√(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=(10+20+25+25+30+40)/(6)\\\\\\Mean=(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=(225+25+0+25+225)/(6)\\\\\\Variance=(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=√(83.33)\\\\Standard\ deviation=9.1285`

Hence, standard deviation=9.1285

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