To find the minimum, first quartile, median, third quartile, and maximum of the given dataset: 20, 70, 13, 15, 23, 17, 40, 51, you need to arrange the data in ascending order first:
13, 15, 17, 20, 23, 40, 51, 70
Now, let's determine the values:
Minimum: The smallest value in the dataset is 13.
First Quartile: This is the median of the lower half of the dataset. In this case, the lower half is {13, 15, 17}. Since the number of elements is odd, the median is the middle value, which is 15.
Median: The median is the middle value of the dataset when it is arranged in ascending order. In this case, the dataset has 8 elements, so the median is the average of the two middle values, which are 20 and 23. Thus, the median is (20 + 23) / 2 = 21.5.
Third Quartile: This is the median of the upper half of the dataset. In this case, the upper half is {40, 51, 70}. Again, the number of elements is odd, so the median is the middle value, which is 51.
Maximum: The largest value in the dataset is 70.
To summarize:
- Minimum: 13
- First Quartile: 15
- Median: 21.5
- Third Quartile: 51
- Maximum: 70