Question #d4932

2 Answers
Aug 26, 2017

See a solution process below:

Explanation:

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"

Aug 26, 2017

3.625°C

Explanation:

Let T_n denote temperature on the nth day. Let M_n denote the mean temperature over the first n days.
Mean for the first seven days is

M_7 = (T_1+T_2+...+T_7)/7

7*M_7 = T_1+T_2+...+T_7

M_8 = (T_1+T_2+...+T_7+T_8)/8

implies M_8 = (7*M_7 + T_8)/8

therefore M_8 = (7*3 + 8)/8 = 29/8 = 3.625°C