Question

the table shows the probabilities of certain prizes in a restaurants contest where the first 100 customers are winners. contest prizes how does the $100 gift card affect the measure of center of the data? 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.

Explanation:

Step1: Recall the effect of an outlier on mean and median

The mean is calculated by summing all values and dividing by the number of values. The median is the middle - value when the data is ordered. A large outlier (like the $100$ gift card) has a greater impact on the mean.

Step2: Analyze the impact on the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The $100$ gift card is a relatively large value compared to other prizes ($1,5,5,10,20$). When we calculate the mean, this large value will increase the sum $\sum_{i = 1}^{n}x_{i}$, and thus increase the mean.

Step3: Analyze the impact on the median

There are $n = 100$ data points. The median is the average of the $50^{th}$ and $51^{st}$ ordered values. Since there are $44$ of the $\$1$ prizes and $25$ of the $\$5$ prizes, the $50^{th}$ and $51^{st}$ values are still $\$5$ (because $44 + 25=69>51$). So the median is not affected by the single $\$100$ gift - card.

Answer:

It increases the mean value of the prizes.