Question

03:20
09:14
05:40
02:14
17:58
13:02
59:06
94:00
To get the exact mean first convert each time to seconds by multiplying the minutes value by 60 and adding this to the seconds. To find the mean in seconds, add up the two times and divide by two. Convert the answer back to minutes and seconds

Answer 1

Let's convert each time into seconds and then find the mean.

1. **03:20**
- Minutes: 3
- Seconds: 20
- Total seconds: \( (3 * 60) + 20 = 180 + 20 = 200 \) seconds

2. **09:14**
- Minutes: 9
- Seconds: 14
- Total seconds: \( (9 * 60) + 14 = 540 + 14 = 554 \) seconds

3. **05:40**
- Minutes: 5
- Seconds: 40
- Total seconds: \( (5 * 60) + 40 = 300 + 40 = 340 \) seconds

4. **02:14**
- Minutes: 2
- Seconds: 14
- Total seconds: \( (2 * 60) + 14 = 120 + 14 = 134 \) seconds

5. **17:58**
- Minutes: 17
- Seconds: 58
- Total seconds: \( (17 * 60) + 58 = 1020 + 58 = 1078 \) seconds

6. **13:02**
- Minutes: 13
- Seconds: 02
- Total seconds: \( (13 * 60) + 2 = 780 + 2 = 782 \) seconds

7. **59:06**
- Minutes: 59
- Seconds: 6
- Total seconds: \( (59 * 60) + 6 = 3540 + 6 = 3546 \) seconds

8. **94:00**
- Minutes: 94
- Seconds: 0
- Total seconds: \( (94 * 60) + 0 = 5640 + 0 = 5640 \) seconds

Now, let's add all these seconds together:

\[ 200 + 554 + 340 + 134 + 1078 + 782 + 3546 + 5640 = 5754 \text{ seconds} \]

Now, we need to find the mean:

There are 8 times:

Mean in seconds = \( \frac{5754}{8} = 719.25 \) seconds

To convert 719.25 seconds back into minutes and seconds:

1. **Minutes** = \( \lfloor \frac{719.25}{60} \rfloor = 11\) minutes
2. **Seconds** = \( 719.25 - (11 * 60) = 719.25 - 660 = 59.25 \) seconds

So, the mean time is approximately **11 minutes and 59.25 seconds**.