Question

3 12 18 12 7 12 6 median: range: mode: mean:

Explanation:

Step1: Sort the data

Sort the numbers \(3,12,18,12,7,12,6\) in ascending order: \(3,6,7,12,12,12,18\).

Step2: Find the median

The median is the middle - value. Since there are \(n = 7\) values, the median is the \(\frac{n + 1}{2}=\frac{7+1}{2}=4^{th}\) value. So the median is \(12\).

Step3: Find the mode

The mode is the most frequently occurring value. The number \(12\) appears \(3\) times, more frequently than other numbers. So the mode is \(12\).

Step4: Find the range

The range is the difference between the maximum and minimum values. The maximum value is \(18\) and the minimum value is \(3\). So the range is \(18−3 = 15\).

Step5: Find the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data points and \(n = 7\). \(\sum_{i=1}^{7}x_{i}=3 + 6+7+12+12+12+18=70\). So the mean is \(\frac{70}{7}=10\).

Answer:

median: \(12\)
range: \(15\)
mode: \(12\)
mean: \(10\)