Answer: The temperature on the fifth day is -14°C
Step-by-step explanation:
When we have a set of N elements, that can be written as:
{a₁, a₂, ..., aₙ}
The mean of these N elements is be written as:
Mₙ = (a₁ + a₂ + ... + aₙ)/N
Now, when we take in account the temperature for the first four days of January, we will have a set of 4 elements, {a₁, a₂, a₃, a₄}
Where each one of these elements represents the temperature of one particular day.
The mean temperature for the first four days will be:
M₄ = (a₁ + a₂ + a₃ + a₄)/4
And we know that this is equal to 4°C
Now we also could do the next replacement:
(a₁ + a₂ + a₃ + a₄) = T
Then we can write:
M₄ = -4°C = (a₁ + a₂ + a₃ + a₄)/4 = T/4
Then we can solve:
-4°C = T/4
-4°C*4 = T
-16°C = T
This is the sum of the temperatures for the first four days of January.
Now we know that the mean for the first five days is -6°C
Then we have:
M₅ = (a₁ + a₂ + a₃ + a₄ + a₅)/5 = -6°C
Where a₅ is the temperature on the fifth day of January, which is the value we want to find.
And we know that:
a₁ + a₂ + a₃ + a₄ = -16°C
We can replace that in the equation to get:
(-16°C + a₅)/5 = -6°C
(-16°C + a₅) = 5*(-6°C) = -30°C
a₅ = -30°C + 16°C = -14°C
a₅ = -14°C
The temperature on the fifth day is -14°C
