2. given the following list of numbers, which of the statements is true? 3, 5, 14, 3, 6, -12, 9 f. average >…

Explanation:

Step1: Arrange the numbers in ascending - order

The list of numbers is (3,5,14,3,6, - 12,9). Arranging them in ascending order gives (-12,3,3,5,6,9,14).

Step2: Calculate the mode

The mode is the number that appears most frequently. Here, the mode is (3) since it appears twice and the other numbers appear only once.

Step3: Calculate the median

There are (n = 7) numbers. The median is the (\left(\frac{n + 1}{2}\right))-th number. So, the median is the (\left(\frac{7+1}{2}\right)=4) - th number. The median is (5).

Step4: Calculate the average

The average (arithmetic mean) (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}), where (\sum_{i=1}^{7}x_{i}=-12 + 3+3+5+6+9+14=28) and (n = 7). So, (\bar{x}=\frac{28}{7}=4).

Step5: Compare the values

We have mode (=3), median ( = 5), average (=4). So, median(>)average(>)mode.

Answer:

J. median > average > mode