Question

Daily high temperatures in the city of Houston for the last week have been: 90, 93, 90 92, 90, 88, 98 (yesterday).

(a) Forecast the high temperature today using a three-day moving average.
(b) Forecast the high temperature today using a two-day moving average.
(c) Calculate the mean absolute deviation based on a two-day moving average, covering all days in which you can have a forecast and an actual temperature.

Answer 1

1. The answer or forecast for temperature using a three-day moving average =
2. The answer or forecast for temperature using a three-day moving average =
3. The mean absolute deviation based on a two-day moving average, covering all days =

Explanation:

1. Three-point averages are calculated by taking a number in the series with the previous and next numbers and averaging the three of them.

Step I - Calculate the three series of succession of numbers form the data and find the average of each of them:

A) (90 + 93 +90)/3 = 91.00

B) (93 + 92 + 90)/3 = 91.67

C) (90 + 92 +90)/3 = 90.67

D) (92 + 90 + 88)/3 = 90.00

E) (90 + 88 + 98)/3 = 92.00

So our series approximated to the nearest whole number is:

91, 92, 91, 90, 92

STEP II

From the series above the highest temperature today is unpredictable because the series is irregular. It went from 91 to 92, then it dropped to 90 and came back to 92.

2. Using a two day moving average we have

STEP I .

Calculate the moving averages

A) (90+93)/2 = 91.50

B) (93 + 90)/2 = 91.50

C) (90 + 92)/2 = 91.00

D) (92 +90)/2 = 91.00

E) (90 + 88)/2 = 89.00

F) (88 + 98)/2 = 93.00

STEP II

The temperature also cannot be predicted because of the irregular series.

3. Calculating the Mean Absolute Deviation based on a two-day moving average

The formula for MAD = (∑|
`x_(i) - \frac{}{x}`|)/
`n`

STEP I

To find the mean absolute deviation of the data, start by finding the mean of the data set.

Mean of the data set =

(91.50 + 91.50 + 91.00 + 91.00 + 89.00 +93.00)/6

Mean = 91.17

STEP II

Get the distance between the data point and the mean:

1. 91.50-91.17=0.33
2. 91.50-91.17= 0.33
3. 91.00-91.17= -0.17
4. 91.00-91.17= -0.17
5. 89.00-91.17= -2.17
6. 90.00-91.17= -1.17

STEP II

Add all the distances together

0.33 + 0.33 - 0.17 - 0.17 - 2.17 - 1.17 = -3.02

STEP III

Divide the the sum by data points

-3.02/6

= -0.50

So on average the temperatures were -0.50 from the mean.

Cheers!

Answer 2

a) The 3-day moving average forecast for today = 92

b) The 2-day moving average forecast for today = 93

c) mean absolute deviation based on a two-day moving average, covering all days in which you can have a forecast and an actual temperature = 1.713

Explanation:

Daily high temperatures in the city of Houston for the last week have been

90, 93, 90 92, 90, 88, 98

a) To forecast the high temperature today using the three-day moving average.

The 3-day moving average involves generating a new set of data by combining the daily high temperature in threes, and then taking the average.

The required forecast is the data generated by combining and taking the average of the last 3 days.

N | T | 3-day moving average

1 | 90 |

2 | 93 |

3 | 90 |

4 | 92 | 91

5 | 90 | 91.6666667

6 | 88 | 90.666667

7 | 98 | 90

The 3-day moving average forecast for today is then given as (90+88+98)/3 = 92

Note that

91 = (90+93+90)/3

91.666667 = (93+90+92)/3

90.666667 = (90+92+90)/3

90 = (92+90+88)/3

92 = (90+88+98)/3

The 3-day moving average forecast for today = 92

b) To forecast the high temperature today using the two-day moving average.

The 2-day moving average involves generating a new set of data by combining the daily high temperature in twos, and then taking the average.

The required forecast is the data generated by combining and taking the average of the last 2 days.

N | T | 2-day moving average

1 | 90 |

2 | 93 |

3 | 90 | 91.5

4 | 92 | 91.5

5 | 90 | 91

6 | 88 | 91

7 | 98 | 89

The 2-day moving average forecastfor today = (88+98)/2 = 93

Just like the calculation in (a),

91.5 = (90+93)/2

91.5 = (93+90)/2

91 = (90+92)/2

And so on....

The 2-day moving average forecast for today is 93.

c) mean absolute deviation based on a two-day moving average, covering all days in which you can have a forecast and an actual temperature.

MAD = Σ/N

μ = mean = (90+93+90+92+90+88+98)/7

μ = 91.57

MAD using the 2-day moving average data will use, 91.5, 91.5, 91, 91, 89 and 93

MAD = [|91.5-91.57| + |91.5-91.57| + |91-91.57| + |91-91.57| + |89-91.57| + |93-91.57|] ÷ 6

MAD = 10.28/6 = 1.713

Hope this Helps!!!