Raven has just started a new job working five days a week in a welding shop. He drives from Camrose to Nisku for work. Raven wants to ensure that he does not arrive late and decides to determine the average length of time it takes for him to drive to work. He records his commuting times, in minutes, for a two-week period.
Time
Day 1. 41
Day 2. 50
Day 3. 42
Day 4. 40
Day 5. 45
Day 6. 75
Day 7. 46
Day 8. 51
Day 9. 30
Day 10. 47
a) Determine the mean commuting time to the nearest tenth.
b) Determine the trimmed mean commuting time to the nearest tenth of a minute.
c) Which mean would be more representative of the number of minutes to commute to work? Justify your answer
a) To find the mean commuting time, we first add up all the commuting times and then divide by the number of days:
Total commuting time = 41 + 50 + 42 + 40 + 45 + 75 + 46 + 51 + 30 + 47 = 467
Mean commuting time = 467 / 10 = 46.7 minutes
So, the mean commuting time is 46.7 minutes.
b) To find the trimmed mean commuting time, we first remove the highest and lowest commuting times, which are 75 and 30, and then find the mean of the remaining commuting times:
Total remaining commuting time = 41 + 50 + 42 + 40 + 45 + 46 + 51 + 47 = 362
Trimmed mean commuting time = 362 / 8 = 45.25 minutes
So, the trimmed mean commuting time is 45.3 minutes.
c) In this case, the trimmed mean commuting time would be more representative of the number of minutes to commute to work. By removing the outliers (the highest and lowest values), we are able to eliminate any extreme values that may skew the average and get a more accurate representation of the typical commuting time for Raven.