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.\ncontest prizes\n| prize | number prizes |\n| ---- | ---- |\n| $1 drink | 44 |\n| $5 meal | 25 |\n| $5 gift card | 15 |\n| $10 gift card | 10 |\n| $20 gift card | 5 |\n| $100 gift card | 1 |\nhow does the $100 gift card affect the measure of center of the data?\no it increases the mean value of the prizes.\no it decreases the mean value of the prizes.\no it increases the median value of the prizes.\no 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.\ncontest prizes\n| prize | number prizes |\n| ---- | ---- |\n| $1 drink | 44 |\n| $5 meal | 25 |\n| $5 gift card | 15 |\n| $10 gift card | 10 |\n| $20 gift card | 5 |\n| $100 gift card | 1 |\nhow does the $100 gift card affect the measure of center of the data?\no it increases the mean value of the prizes.\no it decreases the mean value of the prizes.\no it increases the median value of the prizes.\no it decreases the median value of the prizes.

Answer

Answer:

It increases the mean value of the prizes.

Explanation:

Step1: Recall mean and median concepts

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

Step2: Analyze effect on mean

The $100$ gift - card is a large value. Adding it to the data set will increase the sum of all prize values. Since the number of prizes stays the same, the mean $\frac{\text{Sum of prize values}}{\text{Number of prizes}}$ will increase.

Step3: Analyze effect on median

There are $44 + 25+15 + 10+5 + 1=100$ prizes. The median is the average of the 50th and 51st ordered values. Without the $100$ gift - card, and with the given frequencies, the 50th and 51st values are likely to be $5$ (from the $5$ - dollar meal or $5$ - dollar gift - card). With the $100$ gift - card, the 50th and 51st values are still likely to be $5$ as there are many low - value prizes. So the median is not affected much or may not change at all.