Logo

AskSia

Plus

6. The table below shows the number of tourists who visit a town in October 202...
Apr 25, 2024
6. The table below shows the number of tourists who visit a town in October 2022. Week Number of tourists Mon Tue Wed Thu Fri Sat Sun 1 172 392 432 427 405 655 689 2 192 402 442 438 416 665 701 3 202 414 454 450 428 677 718 4 212 424 467 460 440 686 725 (a) Obtain a suitable moving average trend for the data. (b) Using the additive model, compute the daily seasonal variations.
Solution by Steps
step 1
Calculate the 7-day moving average for the data. This involves taking the average of each consecutive set of 7 days
step 2
For the first 7-day period, the average is 172+392+432+427+405+655+6897\frac{172 + 392 + 432 + 427 + 405 + 655 + 689}{7}
step 3
Continue calculating the 7-day moving averages for all possible consecutive 7-day periods
step 4
Once all 7-day moving averages are calculated, plot them to visualize the trend
Answer
[Insert moving average trend data here]
Key Concept
Moving Average
Explanation
A moving average helps to smooth out fluctuations in data and reveal any underlying trend.
---
step 1
To compute the daily seasonal variations using the additive model, first calculate the average number of tourists for each day of the week
step 2
Subtract the moving average trend value from the actual number of tourists for each corresponding day to find the seasonal variation
step 3
Average these differences for each day of the week to find the average seasonal variation for each day
step 4
These average differences represent the seasonal variations for Monday, Tuesday, Wednesday, etc
Answer
[Insert daily seasonal variations here]
Key Concept
Seasonal Variation in Additive Model
Explanation
In an additive model, the seasonal variation is the difference between the actual value and the trend value for each time period.
What is the formula for calculating a moving average trend in this context?
Solution by Steps
step 1
To calculate a moving average trend, we first decide on the number of periods (n) to include in each average
step 2
We then compute the average for the first n periods to get the first point of the moving average trend
step 3
To find the next point, we drop the first period from the previous set and add the next period to the set, then calculate the average
step 4
We repeat step 3 for all subsequent sets of n periods until we cover the entire data set
Answer
The formula for an n-moving average is si=1n∑j=ii+n−1ajs_i = \frac{1}{n} \sum_{j=i}^{i+n-1} a_j, where sis_i is the moving average at the i-th position, and aja_j are the data points.
Key Concept
Moving Average
Explanation
A moving average helps to smooth out fluctuations in data to identify trends, particularly in time series data. It is calculated by taking the arithmetic mean of a set number of periods or points.
What is the formula for calculating the moving average trend in this context?
Solution by Steps
step 1
To calculate the moving average trend, we first decide on the number of periods (n) to include in the average
step 2
Next, we sum up the data points over the chosen number of periods and divide by n to find the average for each point in the trend
step 3
The formula for an n-moving average is si=1n∑j=ii+n−1ajs_i = \frac{1}{n} \sum_{j=i}^{i+n-1} a_j, where sis_i is the moving average at the i-th position, and aja_j are the data points
step 4
Apply this formula to the given data points to obtain the moving average trend for the specified period
Answer
The moving average trend is calculated using the formula si=1n∑j=ii+n−1ajs_i = \frac{1}{n} \sum_{j=i}^{i+n-1} a_j.
Key Concept
Moving Average Trend
Explanation
The moving average trend smooths out short-term fluctuations and highlights longer-term trends or cycles in the data set. It is calculated by averaging a fixed number of data points and sliding the average across the data set.
© 2023 AskSia.AI all rights reserved