Answer to Question #345206 in Statistics and Probability for Shy

Question

A group of students got the following scores in a test: 6, 9, 12, 15, 18, and 21. Consider samples of size 3 that can be drawn from this population

Answer 1

There are a total of 20 combinations

The samples are

6,9,12

$$Mean =\frac{6+9+12}{3} = 9$$

6,9,15

$$Mean =\frac{6+9+15}{3} = 10$$

6,9,18

$$Mean =\frac{6+9+18}{3} = 11$$

6,9,21

$$Mean =\frac{6+9+21}{3} = 12$$

6,12,15

$$Mean =\frac{6+12+15}{3} = 11$$

6,12,18

$$Mean =\frac{6+12+18}{3} = 12$$

6,12,21

$$Mean =\frac{6+12+21}{3} = 13$$

6,15,18

$$Mean =\frac{6+15+18}{3} = 13$$

6,15,21

$$Mean =\frac{6+15+21}{3} = 14$$

6,18,21

$$Mean =\frac{6+18+21}{3} = 15$$

9,12,15

$$Mean =\frac{9+12+15}{3} = 12$$

9,12,18

$$Mean =\frac{9+12+18}{3} = 13$$

9,12,21

$$Mean =\frac{9+12+21}{3} = 14$$

9,15,18

$$Mean =\frac{9+15+18}{3} = 14$$

9,15,21

$$Mean =\frac{9+15+21}{3} = 15$$

9,18,21

$$Mean =\frac{9+18+21}{3} = 16$$

12,15,18

$$Mean =\frac{12+15+18}{3} = 15$$

12,15,21

$$Mean =\frac{12+15+21}{3} = 16$$

12,18,21

$$Mean =\frac{12+18+21}{3} = 17$$

15,18,21

$$Mean =\frac{15+18+21}{3} = 18$$