What is the median and the 1st or lower quartile of the following data:
4, 12, 15, 20, 24, 30, 32, 35
( 20 + 24 ) / 2 = 44 / 2 = 22
To find the median and the lower quartile of a dataset, you need to follow these steps:
1. Sort the data in ascending order:
The given data set: 4, 12, 15, 20, 24, 30, 32, 35
After sorting: 4, 12, 15, 20, 24, 30, 32, 35
2. Find the median:
- If the data set has an odd number of values, the median is the middle value.
- If the data set has an even number of values, the median is the average of the two middle values.
In this case, the data set has 8 values, so it's an even number. The two middle values are 20 and 24. Therefore, the median is (20 + 24) / 2 = 44 / 2 = 22.
3. Find the lower quartile:
The lower quartile is the median of the lower half of the data set.
In this case, the lower half of the data set is: 4, 12, 15, and 20.
The number of values in the lower half is 4 (an even number), so the two middle values are 12 and 15. The lower quartile is (12 + 15) / 2 = 27 / 2 = 13.5.
Therefore, the median of the given data set is 22, and the lower quartile is 13.5.