Question

question 3
3 pts
a college statistics class conducted a survey of how students spend their money. they asked 25 students to estimate how much money they typically spend each week on fast food. they determined that the mean amount spent on fast food each week is $31.52 and the median is $32. later they realized that a value entered as $2 should have been $20. they recalculate the mean and the median.
which of the following is true?
○ the mean and median will increase.
○ the mean will increase, but the median will remain the same.
○ the mean will stay the same, but the median will increase.
○ both the mean and median will remain the same.

Explanation:

1. Mean Analysis: The mean is calculated as the sum of all values divided by the number of values ($\bar{x}=\frac{\sum x}{n}$). Initially, one value was $2$, and it's corrected to $20$. The change in the sum is $20 - 2=18$. Since $n = 25$ (constant), the new mean will be $\frac{\text{Original Sum}+18}{25}$, which is greater than the original mean. So the mean increases.
2. Median Analysis: The median is the middle value (for $n = 25$, the 13th value when ordered). Correcting $2$ to $20$: if $2$ was below the median (since the original median is $32$), changing $2$ to $20$ does not affect the order of the middle value (the 13th value remains the same). Thus, the median stays unchanged.

Answer:

The mean will increase, but the median will remain the same.