Answer:
Median is a better reflection of how much money the neighborhood kids have.
Step-by-step explanation:
We have been given that 5 kids from the neighborhood are heading to the store to get some snacks. Kid #1 has $1, kid #2 has $2, kid #3 has $3, kid #4 has $4, and kid #5 has $5.
[tex]\text{Mean}=\frac{\text{Sum of all the numbers}}{\text{All the number in data set}}[/tex]
[tex]\text{Mean}=\frac{1+2+3+4+5}{5}[/tex]
[tex]\text{Mean}=\frac{15}{5}[/tex]
[tex]\text{Mean}=3[/tex]
Therefore, the average (mean) amount of cash the five kids have this time is $3.
Median of data set : $1, $2, $3, $4, $5.
Our data set has 5 data points, so median will be the value of 3rd data point, which is 3, therefore, median of data set is $3.
Now let us find mean of data set after the family of kid #5 won the lottery.
[tex]\text{Mean}=\frac{1+2+3+4+5000}{5}[/tex]
[tex]\text{Mean}=\frac{5010}{5}[/tex]
[tex]\text{Mean}=1002[/tex]
Therefore, the mean after replacing $5 by $5,000 will be $1002.
Median of new data set : $1, $2, $3, $4, $5000.
Our new data set has 5 data points, so median will be the value of 3rd data point, which is 3, therefore, median of the new data set is still $3.
Since mean is affected by a very small or large valued data point. We have seen this by the change in kid #5's money as our mean of the money has changed from $3 to $1002, while median remained same, therefore, median is the better reflection of how much money the neighborhood kids have.
