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?\nit increases the mean value of the prizes.\nit decreases the mean value of the prizes.\nit increases the median value of the prizes.\nit decreases the median value of the prizes.
Answer
Explanation:
Step1: Recall mean and median concepts
Mean is sum of values divided by count. 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 stays the same. So, it will increase the mean.
Step3: Analyze the effect on the median
There are a total of $44 + 25+15 + 10+5 + 1=100$ prizes. The median is the average of the 50th and 51st ordered values. Since most of the prizes are lower - value ($1$ drink, $5$ meal, etc.), the 50th and 51st values are likely to be from the lower - value prizes even with the $100$ gift - card. So, the median is not affected much by the $100$ gift - card.
Answer:
It increases the mean value of the prizes.