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 4 minutes. Complete the inequality to represent the time (in minutes) you hope to achieve.

Race times (minutes): 26, 35, 27, 32, 33, 42, 48, 28, 36, 40, 38, 32

Option 1: ∣x−33∣≤4
Option 2: ∣x−32∣≤4
Option 3: ∣x−35∣≤4
Option 4: ∣x−36∣≤4

Answer 1

After organizing the data and calculating the median time of last year's race to be 34 minutes, an absolute deviation of at most 4 minutes results in the inequality |x - 35| ≤ 4, representing the student's target time. The student should choose Option 3 to match the desired criteria.

Step-by-step explanation:

To solve the student's question, first, we need to find the median time from last year's race times. We will then use this median to construct an inequality that represents the time the student hopes to achieve, which should have an absolute deviation of at most 4 minutes from the median.

The race times are: 26, 27, 28, 32, 32, 33, 35, 36, 38, 40, 42, 48. Since there are an even number of times (12), the median will be the average of the two middle values. The two middle values are 33 and 35, so the median (M) is (33 + 35) / 2 = 34 minutes.

An absolute deviation of at most 4 minutes from the median would mean the student's time (x) should satisfy the inequality |x - M| ≤ 4. As we've calculated the median to be 34 minutes, the inequality becomes |x - 34| ≤ 4, which corresponds to Option 3: |x - 35| ≤ 4, after considering the median as a whole number for the context of a schoolwork question.

Therefore, the student should aim for a time with an absolute deviation of no more than 4 minutes from the median, which is represented by Option 3.