Calculate the first, second, and third quartiles of the following samples.
5 8 2 9 5 3 7 4 2 7 4 10 4 3 5 23
To calculate the quartiles of a sample, you need to follow these steps:
1. Sort the sample in ascending order: 2 2 3 3 4 4 4 5 5 5 7 7 8 9 10 23
2. Find the median, which is the middle value of the sorted sample. In this case, there are 16 numbers, so the median is the average of the two middle values: (4 + 5) / 2 = 4.5
3. Split the sample into two halves: the lower half and the upper half. Exclude the median when splitting.
- Lower half: 2 2 3 3 4 4 4 5
- Upper half: 5 5 7 7 8 9 10 23
4. Find the median of the lower half. Since there are 8 numbers, the median is the average of the two middle values: (3 + 4) / 2 = 3.5. This is the first quartile (Q1).
5. Find the median of the upper half. Again, there are 8 numbers, so the median is (7 + 8) / 2 = 7.5. This is the third quartile (Q3).
So, the first quartile (Q1) is 3.5, the second quartile (Q2 - the median) is 4.5, and the third quartile (Q3) is 7.5.
Arrange in order of value, lowest to highest. Second quartile = median.
First quartile is between 4th and 5th score, and third quartile is between 12th and 13th.