find the first quartile, median, third quartile, and the difference of the largest value and the median .

Question

{6, 47, 49, 15, 43, 41, 7, 36}

Answer 1

To find the first quartile (Q1), we need to arrange the data in ascending order:

6, 7, 15, 36, 41, 43, 47, 49

Since there are 8 values, the median is the average of the two middle values, which are 36 and 41. Therefore, the median is:

Median = (36 + 41)/2 = 37.5

To find the third quartile (Q3), we locate the position of the 75th percentile. Since 75% of 8 is 6, we look for the 6th number in the ordered list, which is 47. Therefore, the third quartile is 47.

The difference between the largest value (49) and the median (37.5) is:

Difference = 49 - 37.5 = 11.5

Therefore, the first quartile (Q1) is 15, the median is 37.5, the third quartile (Q3) is 47, and the difference between the largest value and the median is 11.5.