Questions: Module 5 Study Plan: Data Organization Question 2 1 / 3 answered The following numbers are the ages of all eight cousins in the Williams family. Use the data to answer the questions below. 2,11,20,2,2,18,8,15 Round your answers to three decimal places if needed. a. What is the mean age? b. What is the mode? c. What is the median age?

Solution Steps

To solve the given questions about the ages of the Williams family cousins, we will follow these steps:

a. Mean Age: Calculate the mean by summing all the ages and dividing by the number of ages.

b. Mode: Identify the age that appears most frequently in the list.

c. Median Age: Sort the ages and find the middle value. If there is an even number of ages, the median is the average of the two middle numbers.

To find the mean age of the cousins, we sum all the ages and divide by the total number of ages:

\[ \text{Mean} = \frac{2 + 11 + 20 + 2 + 2 + 18 + 8 + 15}{8} = \frac{78}{8} = 9.75 \]

The mode is the age that appears most frequently in the list. In this case, the age \(2\) appears three times, while all other ages appear less frequently. Thus, the mode is:

\[ \text{Mode} = 2 \]

To find the median, we first sort the ages:

\[ 2, 2, 2, 8, 11, 15, 18, 20 \]

Since there are \(8\) ages (an even number), the median is the average of the two middle values:

\[ \text{Median} = \frac{8 + 11}{2} = \frac{19}{2} = 9.5 \]

Final Answer