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.

Step-by-step 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 = (∑||)/

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:

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!

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step-by-step explanation: