Step-by-step explanation:
To find the value where 75% of the data lie above, we need to calculate the third quartile (Q3) as well as the interquartile range (IQR).
First, let's calculate the interquartile range (IQR):
IQR = Q3 - Q1
Given that Q1 = 14 and Q3 = 30.5, we can calculate the IQR:
IQR = 30.5 - 14 = 16.5
Next, to find the value where 75% of the data lie above, we need to add 75% of the IQR to Q3.
Let's calculate 75% of the IQR:
75% of IQR = 0.75 * 16.5 = 12.375
Finally, add 75% of the IQR to Q3 to find the value where 75% of the data lie above:
Q3 + 75% of IQR = 30.5 + 12.375 = 42.875
Therefore, 75% of the data lie above the value 42.875.