Question

Find the mean, the median, and the mode of the collection of numbers shown below. \(57,40,57,57,30,56,40,30,56\)

Short answer

The mean is \(47\), the median is \(56\), and the mode is \(57\).

Step-by-step solution

Calculate the Mean

The mean is calculated by summing up all the numbers and then dividing by the number of numbers. So, for our data set, sum up \(57,40,57,57,30,56,40,30,56\) to get \(423\) and then divide that by the number of numbers, which is \(9\). So, the mean is \(423/9 = 47\).

Calculate the Median

First, the numbers need to be arranged in increasing order: \(30,30,40,40,56,56,57,57,57\). Since the number of values is odd, the median is the middle number, which in this case is \(56\).

Calculate the Mode

The mode of a set is the most frequently occurring number. In our data set, the number \(57\) occurs most frequently, three times, so our mode is \(57\).