Answer:
Mean = 81°F.
S. dev. = 5°F.
Step-by-step explanation:
When we have a set of data:
{x₁, x₂, ..., xₙ}
The mean can be calculated as:
M = (x₁ + x₂ ... + xₙ)/N
Where N is the number of data points that we have:
in this case the set is:
{ 74°F , 79°F , 76°F, 85°F, 87°F, 83°F, 86°F, 78°F }
So N = 8.
Then the mean is:
M = ( 74°F + 79°F + 76°F + 85°F + 87°F + 83°F + 86°F + 78°F )/8
M = 81°F.
Now, the standard deviation can be calculated as.
Sd = √ ( (1/N)*∑(xₐ - M)^2)
where the summation is over xₐ, which represents a summation over all the points in the data set.
Then we can write the standard deviation as:
Sd = √(1/8)*√( (74°F - 81°F)^2 + (79°F - 81°F)^2 + (76°F - 81°F)^2 + (85°F - 81°F)^2 + (87°F - 81°F)^2 + (83°F - 81°F)^2 + (86°F - 81°F)^2 + (78°F - 81°F)^2)
Sd = 4.58°F.
That we should round up to 5°F (because our mean has no digits after the decimal point)
