Final answer:
The mean walking time for the 10 months is 523.3 minutes. The median walking time is 517.5 minutes. To increase the mean by 2 percentage points for the 11 months, you would need to walk 638.426 minutes in November.
Step-by-step explanation:
To calculate the mean walking time for the 10 months, we first add the walking times for each month:
422 + 436 + 445 + 480 + 500 + 535 + 540 + 578 + 587 + 610 = 5233
Now, we divide this sum by the number of months (10) to find the mean:
5233 ÷ 10 = 523.3 minutes
To find the median walking time, we list the times in order:
422, 436, 445, 480, 500, 535, 540, 578, 587, 610
The median is the average of the two middle numbers since there is an even number of data points. Thus, the median is (500 + 535) ÷ 2 = 517.5 minutes.
For part (b), we want the new mean to be 2 percentage points more than the current mean. To find out how much more the new mean needs to be:
523.3 × 0.02 = 10.466 minutes more
Hence, the new mean should be:
523.3 + 10.466 = 533.766 minutes
To find the walking time for November, we multiply the new mean by the new number of months (11) and subtract the sum of the first 10 months:
533.766 × 11 - 5233 = x
x = 5871.426 - 5233 = 638.426 minutes
Therefore, you would have to walk 638.426 minutes in November to meet the new mean.