What is the Mean Absolute Deviation or MAD for each city?

City A: 4, 3.5, 5, 5.5, 4, 2

City B: 5, 6, 3.5, 5.5, 4, 6

Here are the steps to find the MAD

How to find the Mad?
The steps to find the MAD include: 1. find the mean (average). 2. find the difference between each data value and the mean. 3. take the absolute value of each difference. 4. find the mean (average) of these differences.

A: ⅚

B: ⅚

Step-by-step explanation:

City A: 4, 3.5, 5, 5.5, 4, 2

Mean: sum/n

= 24/6 = 4

|x - mean|: 0, 0.5, 1, 1.5, 0 , 2

MAD = sum|x - mean|/n

5/6 = 0.833

City B: 5, 6, 3.5, 5.5, 4, 6

Mean: 30/6 = 5

|x - mean|: 0, 1, 1.5, 0.5, 1, 1

MAD = sum|x - mean|/n

5/6 = 0.833

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt