Final answer:
The mean number of courses taken by the students is 4.2, and the variance of the number of courses is 1.4.
Step-by-step explanation:
The question is asking us to find the mean and variance of the number of courses taken by a small group of students. The list of courses taken is as follows: 3, 4, 5, 6, 3, 4, 5, 6, 3, 3.
- To calculate the mean, sum all the numbers and divide by the total count: (3+4+5+6+3+4+5+6+3+3) / 10 = 42 / 10 = 4.2.
- To calculate the variance, first find the squared differences from the mean, sum them, then divide by the count - 1 (for a sample variance):
- Squared differences: (3-4.2)^2, (4-4.2)^2, (5-4.2)^2, (6-4.2)^2, (3-4.2)^2, (4-4.2)^2, (5-4.2)^2, (6-4.2)^2, (3-4.2)^2, (3-4.2)^2
- Sum of squared differences: 1.44 + 0.04 + 0.64 + 3.24 + 1.44 + 0.04 + 0.64 + 3.24 + 1.44 + 1.44 = 12.6
- Now, divide by the count - 1: 12.6 / (10 - 1) = 12.6 / 9 = 1.4
Therefore, the mean number of courses taken is 4.2 and the variance is 1.4.