A set of data has an interquartile range of 20 and a lower quartile range of 6. if the data is symmetrica, what is the value of the median?

Question

A set of data has an interquartile range of 20 and a lower quartile range of 6. if the data is symmetrica, what is the value of the median?

Please help and explain the outcome..Thanks so much

Answer 1

The key part of the question is that the data is symmetrical. This method only works because the data is symmetrical. So, the IQR = Q3 - Q1 and IQR =20 and Q1 = 6. Using algebra, we can work backwards to first solve Q3. So, 20 = Q3 - 6. Adding 6 to both sides of the equation we solve Q3 to be 26. Next, the median is in the middle of Q3 and Q1 because the data is symmetrical. Find the midpoint of Q3 and Q1 by adding (26 + 6)/2, which is Q2 or the median of the data set. So, the median is 16. You can check the answer by seeing that Q1, Q2, and Q3 are all equidistant from each other or 10 units apart. I hope this helps Michael!