what is the first quartile of the following data set? 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15
To find the first quartile of a data set, you need to arrange the numbers in ascending order and find the median of the lower half.
First, arrange the numbers in ascending order: 11, 15, 15, 15, 16, 17, 18, 19, 20, 22, 23.
Since there are 11 numbers in the data set, the median will be the sixth number: 16.
Next, find the median of the lower half, which is the median of the first five numbers: 11, 15, 15, 15, 16.
To find the median of this sub-group, take the average of the two middle numbers. In this case, the two middle numbers are 15 and 15, so the average is (15 + 15) / 2 = 15.
Therefore, the first quartile of this data set is 15.