Chucky grabbed $11$ items in the grocery store. Each item had a different price, and the mean was about $\$ 4.44$ . On his way to the register, he added a $12^{\text {th }}$ item: a jug of olive oil for $\$ 39.99$ . [show data]. $\newline$ How will adding the jug of olive oil affect the mean and median? $\newline$ Choose $1$ answer: $\newline$ (A) Both the mean and median will increase, but the median will increase by more than the mean. $\newline$ (B) Both the mean and median will increase, but the mean will increase by more than the median. $\newline$ (C) The mean will increase, and the median will decrease. $\newline$ (D) The median will increase, and the mean will decrease.

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Q. Chucky grabbed

11

items in the grocery store. Each item had a different price, and the mean was about

\$ 4.44

. On his way to the register, he added a

12^{\text {th }}

item: a jug of olive oil for

\$ 39.99

. [show data].

\newline

How will adding the jug of olive oil affect the mean and median?

\newline

Choose

1

answer:

\newline

(A) Both the mean and median will increase, but the median will increase by more than the mean.

\newline

(B) Both the mean and median will increase, but the mean will increase by more than the median.

\newline

\newline

(D) The median will increase, and the mean will decrease.

Calculate Total Cost: Calculate the original total cost of the $11$ items before adding the jug of olive oil. $\newline$ Since the mean price of the $11$ items is $\$4.44$ , we can find the total cost by multiplying the mean by the number of items. $\newline$ Total cost = Mean price $\times$ Number of items $\newline$ Total cost = $\$4.44 \times 11$ $\newline$ Total cost = $\$48.84$
Calculate New Total Cost: Calculate the new total cost after adding the jug of olive oil. $\newline$ We add the price of the jug of olive oil to the original total cost to find the new total cost. $\newline$ New total cost = Original total cost + Price of olive oil $\newline$ New total cost = $\$48.84$ + $\$39.99$ $\newline$ New total cost = $\$88.83$
Calculate New Mean Price: Calculate the new mean price after adding the jug of olive oil. $\newline$ The new mean price is the new total cost divided by the new number of items, which is $12$ . $\newline$ New mean price = New total cost / New number of items $\newline$ New mean price = $\$88.83 / 12$ $\newline$ New mean price $\approx \$7.40$
Effect on Median: Determine the effect on the median after adding the jug of olive oil. $\newline$ Since the original number of items was $11$ (an odd number), the median was the price of the $6$ th item when arranged in ascending order. After adding the $12$ th item, the median will be the average of the $6$ th and $7$ th items' prices. If the jug of olive oil is more expensive than at least six of the original items, it will not affect the median because it will be the new highest price, and the median will be the average of the original $6$ th and $7$ th items' prices. However, since we do not have the individual prices of the original items, we cannot determine the exact median but can infer that it will either stay the same or increase.
Choose Correct Answer: Choose the correct answer based on the calculations. $\newline$ From Step $3$ , we know that the mean will increase from $\$4.44$ to approximately $\$7.40$ . From Step $4$ , we know that the median will either stay the same or increase, but not decrease. Therefore, the correct answer is that both the mean and median will increase, but the mean will increase by more than the median because the addition of the jug of olive oil significantly increases the total cost, which has a greater effect on the mean than on the median.