Question

The mean temperature for the first 4 days in January was - 4 degrees the mean temperature for the first 5 days in January was - 6

degrees what was the temperature on the 5th day​

Answer 1

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.