Question

Suppose that, as done in some lotteries, we sample balls from a large vessel. The vessel contains a large number of balls, each labeled from a single number, 0-9. There are an equal number of balls for each number, and the balls are continually being mixed. For this example, lets collect 10 samples of three balls each. Each sample is formed by selecting balls one at a time and replacing each ball back in the vessel before selecting the next ball. The selection process used ensures that every ball in the vessel has an equal chance of being chosen on each selection. Assume the following samples are collected.

1,3,4,3,4,7 2,2,6,1,2,6 3,8,8,2,3,7 1,6,7,6,8,9 5,6,9,4,7,9  

a. Calculate the mean of each sample.

b. Calculate the median of each sample.

Answer 1

For this problem, since the sample sizes are 3 in all the cases, the formula for mean is: .

In case of median, we arrange the 3 units in each of the samples in ascending order and then choose the middle-most value.

Sample 1:
1,3,4
Mean = 2.67, Median = 3

Sample 2:
3,4,7
Mean = 4.67, Median = 4

Sample 3:
2,2,6
Mean = 3.33, Median = 2

Sample 4:
1,2,6
Mean = 3, Median = 2

Sample 5:
3,8,8
Mean = 6.33, Median = 8

Sample 6:
2,3,7
Mean = 4, Median = 3

Sample 7:
1,6,7
Mean = 4.67, Median = 6

Sample 8:
6,8,9
Mean = 3.83, Median = 8

Sample 9:
5,6,9
Mean = 6.67, Median = 6

Sample 10:
4,7,9
Mean = 6.67, Median = 7