Answer: The temperature on the 5th day is -14 degrees.
Explanation:
If we have a set of N values:
{x₁, x₂, x₃, ..., xₙ}
The mean value of this set is:
M = (x₁ + x₂ + ... + xₙ)/N
Now, we know that the mean temperature for the first 4 days of January is -4°
Then if the temperatures for the first four days are {T₁, T₂, T₃, T₄}
We have:
M₄ = (T₁ + T₂ + T₃ + T₄)/4 = -4°
Where we can replace (T₁ + T₂ + T₃ + T₄) by K
Then:
K/4 = -4°
K = -4°*4 = -16°
Is the sum of the temperatures for the first four days.
Now when we consider the first 5 days, the mean is -6°, and let's define T₅ as the temperature of the fifth day, then we get:
M₅ = -6° = (T₁ + T₂ + T₃ + T₄ + T₅)/5
And we know that:
(T₁ + T₂ + T₃ + T₄) = K = -16°
We can replace that in the above equation to get:
M₅ = (-16° + T₅)/5 = -6°
Now we can solve this for T₅
(-16° + T₅) = 5*(-6°) = -30°
T₅ = -30° + 16° = -14°
T₅ = -14°
The temperature on the 5th day is -14 degrees.