Answer:
The mean average monthly temperature in City 1 is 48.75°F.
The mean absolute deviation for the average monthly temperature in City 1 is 13.375°F
Step-by-step explanation:
For this case we have the following dataset given:
Average Monthly Temperatures for City 1 (° F)
30, 38, 66, 78, 47, 75, 35, 45, 56, 29, 49, 37
Average Monthly Temperatures for City 2 (° F)
15, 23, 51, 63, 32, 60, 20, 30, 41, 14, 34, 22
For this case the sample mean can be calculated with the following formula:
![$\bar{X}=\frac{\sum_{i=1}^{n} x_{i}}{n}$](https://tex.z-dn.net/?f=%24%5Cbar%7BX%7D%3D%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20x_%7Bi%7D%7D%7Bn%7D%24)
And replacing we got:
![$\bar{X}_{1}=\frac{30+38+66+78+47+75+35+45+56+29+49+37}{12}=48.75$](https://tex.z-dn.net/?f=%24%5Cbar%7BX%7D_%7B1%7D%3D%5Cfrac%7B30%2B38%2B66%2B78%2B47%2B75%2B35%2B45%2B56%2B29%2B49%2B37%7D%7B12%7D%3D48.75%24)
The mean average monthly temperature in City 1 is 48.75°F.
And now we can calculate the following values:
![$|38-48.75|=10.75$](https://tex.z-dn.net/?f=%24%7C38-48.75%7C%3D10.75%24)
![$|66-48.75|=17.25$](https://tex.z-dn.net/?f=%24%7C66-48.75%7C%3D17.25%24)
![$|78-48.75|=29.25$](https://tex.z-dn.net/?f=%24%7C78-48.75%7C%3D29.25%24)
![$|47-48.75|=1.75$](https://tex.z-dn.net/?f=%24%7C47-48.75%7C%3D1.75%24)
![$|75-48.75|=26.25$](https://tex.z-dn.net/?f=%24%7C75-48.75%7C%3D26.25%24)
![$|35-48.75|=13.75$](https://tex.z-dn.net/?f=%24%7C35-48.75%7C%3D13.75%24)
![$|45-48.75|=3.75$](https://tex.z-dn.net/?f=%24%7C45-48.75%7C%3D3.75%24)
![$|56-48.75|=7.25$](https://tex.z-dn.net/?f=%24%7C56-48.75%7C%3D7.25%24)
![$|29-48.75|=19.75$](https://tex.z-dn.net/?f=%24%7C29-48.75%7C%3D19.75%24)
![$|49-48.75|=0.25$](https://tex.z-dn.net/?f=%24%7C49-48.75%7C%3D0.25%24)
![$|37-48.75|=11.75$](https://tex.z-dn.net/?f=%24%7C37-48.75%7C%3D11.75%24)
And the mean absolute deviation is given by:
![$M A D=\frac{\sum_{i=1}^{n}\left|X_{i}-\bar{X}\right|}{n}=\frac{160.5}{12}=13.375$](https://tex.z-dn.net/?f=%24M%20A%20D%3D%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%5Cleft%7CX_%7Bi%7D-%5Cbar%7BX%7D%5Cright%7C%7D%7Bn%7D%3D%5Cfrac%7B160.5%7D%7B12%7D%3D13.375%24)
The mean absolute deviation for the average monthly temperature in City 1 is 13.375°F