Question

Find the mean, the median, and the mode of the collection of numbers. $$2,2,2,2,4,4,5$$

Short answer

The mean of the collection of numbers is 3, the median is 2, and the mode is 2.

Step-by-step solution

Calculate the Mean

First, add up all the numbers \(2 + 2 + 2 + 2 + 4 + 4 + 5 = 21\). Then, divide this sum by the total number of data points (7) to get the mean. \(21 \div 7 = 3\). The mean of the set is 3.

Calculate the Median

To find the median, list the numbers in numerical order, and find the middle number. If there is an even number of observations, take the average of the two middle numbers. Here, the numbers are already in order and there is an odd number of observations, so the median is simply the fourth number: 2.

Calculate the Mode

The mode is the number that appears most frequently in the data set. In this case, the number 2 appears four times, which is more than any other number. So, the mode is 2.