Question

a group of 6 friends shared their weekly allowances: $20, $25, $30, $35, $40, $120. the mean allowance is $45, while the median is $32.50. what can be inferred about their allowances? one or more friends receive a significantly larger allowance than the others. one or more friends receive a significantly smaller allowance than the others. the allowances are uniformly distributed among the friends. most of the friends have allowances close to the mean of $45.

Explanation:

Step1: Understand mean and median

The mean is the sum of all values divided by the number of values. The median is the middle - value when the data is ordered. For 6 values, the median is the average of the 3rd and 4th ordered values.

Step2: Analyze the given data

The values are $20, 25, 30, 35, 40, 120$. The mean is $\frac{20 + 25+30 + 35+40+120}{6}=\frac{270}{6}=45$. The median of $20, 25, 30, 35, 40, 120$ is $\frac{30 + 35}{2}=32.5$. The value 120 is much larger than the other values. This large value (outlier) pulls the mean up.

Answer:

One or more friends receive a significantly larger allowance than the others.