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 the concept of mean

Mean is the sum of all values divided by the number of values. The $100$ gift - card is a large - valued outlier. Adding a large value to the data set will increase the sum of all values while the number of values only increases by 1. So, it will increase the mean.

Step2: Recall the concept of median

There are a total of $44 + 25+15 + 10+5 + 1=100$ data points. The median of 100 data points is the average of the 50th and 51st ordered data points. Without the $100$ gift - card, we order the prizes by value and frequency. The 50th and 51st values are likely to be in the $5$ meal or $5$ gift - card range. Even with the $100$ gift - card added, the 50th and 51st ordered data points will not be affected by this single large value. So, the median is not affected.

Answer:

It increases the mean value of the prizes