the table shows the probabilities of certain prizes in a restaurants contest where the first 100 customers…

the table shows the probabilities of certain prizes in a restaurants contest where the first 100 customers are winners. how does the $100 gift card affect the measure of center of the data? contest prizes prize number prizes $1 drink 44 $5 meal 25 $5 gift card 15 $10 gift card 10 $20 gift card 5 $100 gift card 1 it increases the mean value of the prizes. it decreases the mean value of the prizes. it increases the median value of the prizes. it decreases the median value of the prizes.

the table shows the probabilities of certain prizes in a restaurants contest where the first 100 customers are winners. how does the $100 gift card affect the measure of center of the data? contest prizes prize number prizes $1 drink 44 $5 meal 25 $5 gift card 15 $10 gift card 10 $20 gift card 5 $100 gift card 1 it increases the mean value of the prizes. it decreases the mean value of the prizes. it increases the median value of the prizes. it decreases the median value of the prizes.

Answer

Explanation:

Step1: Recall mean and median concepts

Mean is sum of values divided by number of values. Median is middle - value when data is ordered.

Step2: Analyze the effect on the mean

The $100$ gift - card is a large value. When calculating the mean, this large value will increase the sum of all prize values while the number of prizes remains the same. So, it will increase the mean.

Step3: Analyze the effect on the median

There are $44 + 25+15 + 10+5 + 1=100$ prizes. The median is the average of the 50th and 51st ordered values. Since there are 44 $1$ - dollar drinks and 25 $5$ - dollar meals ($44 + 25=69$), the 50th and 51st values are both $5$ - dollar meals. Adding the single $100$ gift - card does not change the position of the middle values. So, the median remains the same.

Answer:

It increases the mean value of the prizes.