The problem asks us to find the mean and median of the set of numbers: $1, 3, 3, 3, 4, 6, 99$. We are also asked to determine which average (mean or median) best describes the set of numbers.

1. Problem Description

The problem asks us to find the mean and median of the set of numbers: $1, 3, 3, 3, 4, 6, 99$. We are also asked to determine which average (mean or median) best describes the set of numbers.

2. Solution Steps

First, we find the mean of the set of numbers. The mean is calculated by summing all the numbers in the set and dividing by the total number of elements in the set.

Mean = $\frac{1 + 3 + 3 + 3 + 4 + 6 + 99}{7} = \frac{119}{7} = 17$

Next, we find the median of the set of numbers. The median is the middle value when the numbers are arranged in ascending order. In this case, the numbers are already in ascending order. Since there are 7 numbers in the set, the median is the 4th number.

Median = 3

To determine which average best describes the set of numbers, we consider whether the mean is heavily influenced by outliers. In this case, the number 99 is a large outlier compared to the other numbers. This outlier significantly increases the mean. Therefore, the median is a better representation of the typical value in the set because it is not affected by the outlier.

3. Final Answer

Mean = 17

Median = 3

The median best describes the set of numbers.