Answer:
The lower quartile is 23.4
Explanation:
The given data are;
47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4
Rearranging the data, we have;
5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4, 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2
The lower quartile, Q₁, is the (n + 1)/4 th term which is (16 +1)/4 = 4.25th term
However since we have an even set of numbers, we place a separator at the middle and we look for the median of the left half as follows
5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4║ 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2
We have two numbers (17.4 + 29.4) at the median of the left set of numbers, we find the average of the two numbers to get the lower quartile
The lower quartile is therefore = (17.4 + 29.4)/2 = 23.4.