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KatRina [158]
3 years ago
14

The forecast for week 13 is 747. ​(Enter your response rounded to the nearest whole​ number.) Specify the mean absolute deviatio

n​ (MAD) and mean absolute percent error​ (MAPE). ​(Enter your responses rounded to two decimal​ places.)
Mathematics
1 answer:
son4ous [18]3 years ago
7 0

Answer:

a) MAD without the forecast = 43.71

MAD with the forecast = 45.59

b) MAPE = 0.097 = 9.7%

Step-by-step explanation:

642 602 656 747 663 618 731 726 679 737 664 740

Mean Absolute deviation is given as

MAD = [Σ|x - μ|]/N

We first calculate the mean

Mean = Σx/N

Mean = (642+602+656+747+663+618+731+726+679+737+664+740)/12

Mean = (8205/12) = 683.75

absolute deviations from the mean

|642-683.75| + |602-683.75| + |656-683.75| + |747-683.75| + |663-683.75| + |618-683.75| + |731-683.75| + |726-683.75| + |679-683.75| + |737-683.75| + |664-683.75| + |740-683.75|

Absolute deviations from the mean

41.75+81.75+27.75+63.25+20.75+65.75+47.25+42.25+4.75+53.25+19.75+56.25

= 524.5

MAD = [Σ|x - μ|]/N

MAD = (524.5/12)

MAD = 43.71

If we include the forecast on the 13th week

642 602 656 747 663 618 731 726 679 737 664 740 747

Mean = (8205+747)/13

Mean = 688.62

absolute deviations from the mean

|642-688.62| + |602-688.62| + |656-688.62| + |747-688.62| + |663-688.62| + |618-688.62| + |731-688.62| + |726-688.62| + |679-688.62| + |737-688.62| + |664-688.62| + |740-688.62| + |747-688.62|

Absolute deviations from the mean

= 46.62+86.62+32.62+58.38+25.62+70.62+42.38+37.38+9.62+48.38+24.62+51.38+58.38

= 592.62

MAD = (592.62/13)

MAD = 45.59.

b) MAPE is used to check forecast errors

MAPE = (1/N) Σ [|x-f|/x]

where N = Sample size = 12

x = each variable

f = the forecasted value = 747

x = 642, 602, 656, 747, 663, 618, 731, 726, 679, 737, 664, 740

Σ [|x-f|/x]

= 0.164+0.241+0.139+0+0.112+0.209+0.022+0.029+0.100+0.014+0.125+0.009

Σ [|x-f|/x] = 1.164

MAPE = (1.164/12)

MAPE = 0.097 = 9.7%

Hope this Helps!!!

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Answer:

12-[20-2(6^2\div3\times2^2)]=88

Step-by-step explanation:

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12-[20-2(6^2\div3\times2^2)]

Recall the order of operations or PEMDAS:

P: Operations within parentheses must be done first. On a side note, do parentheses before brackets.

E: Within the parentheses, if exponents are present, do them before all other operations.

M/D: Multiplication and division next, whichever comes first.

A/S: Addition and subtraction next, whichever comes first.

(Note: This is how the order of operations is traditionally taught and how it was to me. If this is different for you, I do apologize. However, the answer should be the same.)

Thus, we should do the operations inside the parentheses first. Therefore:

12-[20-2(6^2\div3\times2^2)]

The parentheses is:

(6^2\div3\times2^2)

Square the 6 and the 4:

(36\div3\times4)

Do the operations from left to right. 36 divided by 3 is 12. 12 times 4 is 48:

(36\div3\times4)\\=(12\times4)\\=48

Therefore, the original equation is now:

12-[20-2(6^2\div3\times2^2)]\\=12- [20-2(48)]

Multiply with the brackets:

=12-[20-96]

Subtract with the brackets:

=12-[-76]

Two negatives make a positive. Add:

=12+76=88

Therefore:

12-[20-2(6^2\div3\times2^2)]=88

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