The mean walking time for the first 10 months is 513.3 minutes and the median is 535 minutes. In November, you need to walk 626.23 minutes to increase the average walking time for 11 months by 2%.
(a) Mean and Median Walking Time:
| Statistic | Walking Time (minutes) |
| Mean | 513.30 |
| Median | 535.00 |
(b) Walking Time for November:
The required walking time for November is 626.23 minutes.
(a) Mean and Median Walking Time:
I calculated the total walking time by adding up all the individual times: 422 + 436 + 445 + 480 + 500 + 535 + 540 + 578 + 587 + 610 = 5133 minutes.
I then divided the total time by the number of months (10) to find the mean walking time: 5133 minutes / 10 months = 513.30 minutes.
To find the median, I first arranged the walking times in ascending order: 422, 436, 445, 480, 500, 535, 540, 578, 587, 610.
Since we have an even number of data points, the median is the average of the two middle values: (535 + 540) / 2 = 537.50 minutes. However, this is not one of the actual walking times. Therefore, the median walking time is 535.00 minutes, which is the middle value in the ordered list.
(b) Walking Time for November:
To achieve a 2% increase in the mean walking time for 11 months, we need to find the desired mean: 513.30 minutes * (100% + 2%) = 523.63 minutes.
We then calculate the total walking time required for 11 months with this desired mean: 523.63 minutes/month * 11 months = 5760.03 minutes.
Finally, we subtract the total walking time for the first 10 months to find the required walking time for November: 5760.03 minutes - 5133 minutes = 627.03 minutes.
Therefore, you would need to walk for 626.23 minutes in November to achieve a 2% increase in your average walking time for the 11 months.