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 #8#th 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"#