Questions: Find the mean, median, and mode for the following data set. 38 76 22 76 99 43 (a) Find the mean. Round your answer to one decimal place, if necessary. Mean = (b) Find the median. Round your answer to one decimal place, if necessary. Median =

Solution Steps

To solve this problem, we need to calculate the mean, median, and mode of the given data set.

1. Mean: Sum all the numbers and divide by the count of numbers.
2. Median: Sort the numbers and find the middle value. If the count is even, average the two middle numbers.
3. Mode: Identify the number that appears most frequently.

The mean is calculated by summing all the numbers in the data set and dividing by the number of elements.

Given data: \(38, 76, 22, 76, 99, 43\)

\[ \text{Mean} = \frac{38 + 76 + 22 + 76 + 99 + 43}{6} = \frac{354}{6} = 59 \]

To find the median, first sort the data set and then find the middle value. If the number of elements is even, average the two middle numbers.

Sorted data: \(22, 38, 43, 76, 76, 99\)

Since there are 6 numbers, the median is the average of the 3rd and 4th numbers:

\[ \text{Median} = \frac{43 + 76}{2} = \frac{119}{2} = 59.5 \]

The mode is the number that appears most frequently in the data set.

In the given data, \(76\) appears twice, while all other numbers appear only once.

\[ \text{Mode} = 76 \]

Final Answer