algebra homework help

Question

You are competing in a race. The table shows the times from last year's race. You want your time to be last year's median time with an absolute deviation of at most 5 minutes. Complete the inequality to represent the time (in minutes) you hope to achieve.

Race times (minutes)
74	65	57	62
63	72	78	58
60	70	68	62

Answer 1

The best way to approach finding the median in a large group of numbers like this is to write them down in sequential order. From lowest to highest: 57, 58, 60, 62, 62, 63, 65, 68, 70, 72, 74, 78. With 12 values, the median will be calculated by averaging the two middle values (6th from the lowest and 6th from the highest). These values are 63 and 65 respectively. So, the median time is 64 minutes. If your time must be within 5 minutes of this value, and we treat the goal time as x, the inequality can be written as 59 ≤ x ≤ 69.