The mean is calculated by adding a set of values and then dividing the sum by the number of values added. The formula is:
A = s/n
Where:
A is the median or average. For the first 7 days in January we are told this is 3^o"C"
s is the sum of the numbers. What we will solve for in this part of the problem.
n is the number of numbers. 7 for this problem for the first 7 days in January.
Substituting and solving for s gives:
3^o"C" = s/7
color(red)(7) xx 3^o"C" = color(red)(7) xx s/7
21^o"C" = cancel(color(red)(7)) xx s/color(red)(cancel(color(black)(7)))
21^o"C" = s
s = 21^o"C" +
To determine the mean for the 8 days we need to find the sum of the temperatures for the 8 days and divide by the number of days, which will now be 8.
To find the sum of the 8 days, we take the sum of the first 7 days which we just calculated and add the temperature from the 8th day.
s_8 = 21^o"C" + 8^o"C" = 29^o"C"
Substituting this new sum and dividing by 8 days gives:
A = (29^o"C")/8
A = 3.625^o"C"
The mean temperature for the first 8 days in January is: 3.625^o"C"