Question

finding mode, median, mean
find the mode, median, and mean for

1. goals in a hockey game med

1 3 6 5 9 2 5 3
6 3 5

Explanation:

Step1: Sort the data

Sort the data set \(1,3,6,5,9,2,5,3,6,3,5\) in ascending order: \(1,2,3,3,3,5,5,5,6,6,9\)

Step2: Find the mode

The mode is the number that appears most frequently. Here, \(3\) appears \(3\) times and \(5\) appears \(3\) times.

Step3: Find the median

The median is the middle number. Since there are \(n = 11\) numbers (odd), the median is the \(\frac{n + 1}{2}=\frac{11+ 1}{2}=6^{th}\) number. The \(6^{th}\) number in the sorted list is \(5\)

Step4: Find the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). \(\sum_{i=1}^{11}x_{i}=1+2 + 3+3+3+5+5+5+6+6+9=48\), \(n = 11\). So \(\bar{x}=\frac{48}{11}\approx4.36\)

Answer:

Mode: \(3\) and \(5\); Median: \(5\); Mean: \(\frac{48}{11}\approx4.36\)