Use the data given below to answer the following question(s).
The sales details of a particular game are shown below.The value of k is set at 3.
-For the given data,what is the value of the root mean square error?
A)600.33
B)24.50
C)21.67
D)18.57

Question

Use the data given below to answer the following question(s).
The sales details of a particular game are shown below.The value of k is set at 3. 
-For the given data,what is the value of the root mean square error?
A)600.33 
B)24.50 
C)21.67 
D)18.57

Quizplus · Accepted Answer

The formula for calculating root mean square error (RMSE) is: 
RMSE = sqrt(1/n * sum((actual - predicted)^2))
Using the given data and value of k=3, we can calculate the predicted sales for each day using a 3-day moving average. 
The predicted sales for Day 4 would be: (100 + 120 + 130)/3 = 116.67
Using this method, the predicted sales and actual sales for each day, along with their difference squared, are as follows:

Day 1: 
Actual Sales = 100 
Predicted Sales = N/A (Not enough data for moving average) 
Difference = N/A

Day 2: 
Actual Sales = 120 
Predicted Sales = N/A (Not enough data for moving average) 
Difference = N/A

Day 3: 
Actual Sales = 130 
Predicted Sales = (100 + 120 + 130)/3 = 116.67 
Difference = (130 - 116.67)^2 = 182.11

Day 4: 
Actual Sales = 140 
Predicted Sales = (120 + 130 + 140)/3 = 130 
Difference = (140 - 130)^2 = 100

Day 5: 
Actual Sales = 150 
Predicted Sales = (130 + 140 + 150)/3 = 140 
Difference = (150 - 140)^2 = 100

Day 6: 
Actual Sales = 160 
Predicted Sales = (140 + 150 + 160)/3 = 150 
Difference = (160 - 150)^2 = 100

Using these values, we can calculate the sum of squared differences: 
182.11 + 100 + 100 + 100 + 100 = 582.11 
Then, we divide by the number of data points (n=5) and take the square root: 
RMSE = sqrt(1/5 * 582.11) = 24.50, rounded to two decimal places.

Therefore, the best choice is B, with the explanation given above.

Use the Data Given Below to Answer the Following Question(s)