In the data set below, what is the upper quartile?
2 2 2 5 2 7 3 5 5 1 7 4 8 0
To find the upper quartile, we first need to order the data set from least to greatest:
0 1 2 2 2 2 3 4 5 5 5 7 7 8
Next, we calculate the median of the upper half of the data set. In this case, the upper half is:
5 5 5 7 7 8
The median of this upper half is the upper quartile. Since there are 6 elements in the upper half, the median will be the average of the two middle numbers, which are 5 and 7.
(5 + 7) / 2 = 12 / 2 = 6
Therefore, the upper quartile is 6.
In the data set below, what is the lower quartile?
1 4 1 6 2 6 3 3 4 8
To find the lower quartile, we first need to order the data set from least to greatest:
1 1 2 3 3 4 4 6 6 8
Next, we calculate the median of the lower half of the data set. In this case, the lower half is:
1 1 2 3 3
The median of this lower half is the lower quartile. Since there are 5 elements in the lower half, the median will be the middle number, which is 2.
Therefore, the lower quartile is 2.
To find the upper quartile in a data set, you need to first put the data in ascending order. Here is the data set sorted in ascending order: 0 1 2 2 2 2 3 4 5 5 5 7 7 8.
The upper quartile divides the data into four parts, where roughly 25% of the data is below it and 75% is above it. To find the upper quartile, you need to determine the value that is three-quarters of the way through the sorted data set.
To do this, you need to find the index position of the upper quartile. Since there are 14 numbers in the data set, the index position of the upper quartile can be calculated as (14 + 1) * (3 / 4) = 11.25. Since we cannot have a fractional index position, we can round up to the nearest whole number, which in this case is 12.
The value at index position 12 is 7. Therefore, the upper quartile in this data set is 7.