(a) If the median of the data \( 13,14, p, 17,20 \) which are arranged in ascending order is 16 , find the value of \( p \). (b) If the median of the data \( 400,350,300, q, 200,150,100 \) which are arranged in descending order is 250 , find the value of \( q \).

To find \( p \) in the first dataset \( 13, 14, p, 17, 20 \) arranged in ascending order with a median of 16, you must consider how the median is defined in a 5-number list. The median is the middle number, so for the arrangement \( 13, 14, p, 17, 20 \), \( p \) must be greater than 14 but less than 17. Given the median is 16, it follows that \( p = 16 \). For the second dataset \( 400, 350, 300, q, 200, 150, 100 \) arranged in descending order with a median of 250, there are 7 numbers, so the median will be the fourth number. We know \( q \) must fit into this arrangement, leading to the sequence \( 400, 350, 300, q, 200, 150, 100 \). For the median to be 250, it must be placed between 300 and 200. Thus, \( q \) should be \( 250 \) to correctly satisfy this median position.