Question:
Chucky grabbed 11 items in the grocery store that each had a different price and had a mean cost of about $4.44. On his way to the register, he gave in to an impulse to add a 12th item: an entire wheel of cheese that cost $39.99.
How will adding the wheel of cheese affect the mean and median?
Answer:
There will be a big difference in the mean when the new item is added
Step-by-step explanation:
Given
[tex]Items = 11[/tex]
[tex]Mean = \$4.44[/tex]
Before we solve further, we need to first calculate the total amount of the 11 items.
[tex]Mean = \frac{Total}{Items}[/tex]
Make Total the Subject of formula
[tex]Total = Mean * Items[/tex]
[tex]Total = \$4.44 * 11[/tex]
[tex]Total = \$48.84[/tex]
When the 12th item of $39.99 is added, the new mean becomes.
[tex]New\ Mean = \frac{Total + \$39.99}{11 + 1}[/tex]
[tex]New\ Mean = \frac{\$48.84 + \$39.99}{11 + 1}[/tex]
[tex]New\ Mean = \frac{\$88.83}{12}[/tex]
[tex]New\ Mean = \$7.4025[/tex]
By comparing this the old mean, we can see a huge increment between $4.44 and $7.4025
This means that there will be a big difference in the mean when the new item is added.
For the Median:
The old mean shows that the prices of the 11 items is within a small range from $4.44.
So, when the new item is added the median will only change a little bit.
In other words, the median value will only change a little bit.
