Consider the time series graphs drawn below, along with two sets of moving averages. For each graph, explain which moving average is most appropriate for this data.
Consider the time series data displayed in the table:
Calculate the values of a, b, c and d, correct to one decimal place
Use your calculator to find the following correct to four decimal places:
The correlation coefficient for the raw data.
The correlation coefficient for the 3 point moving average data.
Is the correlation coefficient stronger for the raw data or the 3 point moving average data?
| \text{Time period} | \text{Raw data} | 3 \text{ point} \\\\\ \text{moving average} |
|---|---|---|
| 1 | 3.9 | |
| 2 | 3.9 | 13 |
| 3 | 31.3 | a |
| 4 | 3.8 | 13.9 |
| 5 | 6.6 | 14.9 |
| 6 | 34.4 | b |
| 7 | 6.1 | 16.4 |
| 8 | 8.6 | 15.6 |
| 9 | c | 17 |
| 10 | 10.3 | 18.1 |
| 11 | 11.8 | 20.4 |
| 12 | d |
For each of the tables below that contain time series data:
Calculate the values of a, b, c and d, correct to one decimal place.
Determine which moving average best smooths the data.
| \text{Time period} | \text{Raw data} | \text{3-moving average} | \text{5-moving average} |
|---|---|---|---|
| 1 | 113.8 | ||
| 2 | 109 | 112.1 | |
| 3 | 113.4 | 107.4 | 97.7 |
| 4 | 99.7 | a | b |
| 5 | 52.6 | 86.4 | 93.8 |
| 6 | 107 | 85.3 | 91.6 |
| 7 | 96.3 | 101.8 | 90.7 |
| 8 | c | 98 | 89.5 |
| 9 | 95.6 | 81.4 | 88.2 |
| 10 | 46.5 | 80.9 | 86.7 |
| 11 | 100.5 | 78.6 | |
| 12 | d |
| \text{Time period} | \text{Raw data} | \text{3-moving average} | \text{5-moving average} |
|---|---|---|---|
| 1 | 43.8 | ||
| 2 | 46.5 | 41.2 | |
| 3 | 33.4 | 41 | 42.5 |
| 4 | 43 | a | b |
| 5 | 45.8 | 40.5 | 39.4 |
| 6 | 32.8 | 40.3 | 41.8 |
| 7 | 42.2 | 40 | 39.6 |
| 8 | c | 39.9 | 38.7 |
| 9 | 32.3 | 39.6 | 41.1 |
| 10 | 41.3 | 39.5 | 39 |
| 11 | 44.8 | 39.2 | |
| 12 | d |
| \text{Time period} | \text{Raw data} | \text{3-moving average} | \text{5-moving average} |
|---|---|---|---|
| 1 | 43.6 | ||
| 2 | 35.3 | 37.2 | |
| 3 | 32.7 | 39.6 | 42.6 |
| 4 | 50.8 | a | b |
| 5 | 50.6 | 50.8 | 45.6 |
| 6 | 51 | 48.1 | 46.2 |
| 7 | 42.7 | 43.1 | 47 |
| 8 | c | 44.4 | 47.7 |
| 9 | 54.9 | 48.2 | 47.9 |
| 10 | 54.1 | 53.8 | 48.2 |
| 11 | 52.3 | 50.2 | |
| 12 | d |
Consider the time series data displayed in the table:
Calculate the values of a and b correct to two decimal places.
Calculate the values of c and d correct to one decimal place.
Use your calculator to find the following correct to four decimal places:
The correlation coefficient for the raw data.
The correlation coefficient for 4 point moving average data.
Is the correlation coefficient stronger for the raw data or the 4 point moving average data?
| \text{Time period} | \text{Raw data} | \text{4 point centred}\\\text{moving average} |
|---|---|---|
| 1 | 29.7 | |
| 2 | 14.9 | |
| 3 | 9.2 | a |
| 4 | 31.1 | 23.03 |
| 5 | 34.9 | 24.68 |
| 6 | 18.9 | b |
| 7 | 18.4 | 26.98 |
| 8 | 34.5 | 27.99 |
| 9 | c | 28.56 |
| 10 | 24.6 | 29.05 |
| 11 | 17.3 | |
| 12 | d |
Consider the time series data displayed in the table:
Find the value of x in the table. Give your answer to two decimal places.
Find for the value of y in the table. Give your answer to one decimal place.
Use your calculator to find the following correct to four decimal places:
The correlation coefficient for the raw data.
The correlation coefficient for the 6 point centred moving average data.
Is the correlation coefficient stronger for the raw data or the 6 point moving average data?
| \text{Time period} | \text{Raw data} | \text{6 point centred} \\\ \text{moving average} |
|---|---|---|
| 1 | 21.9 | |
| 2 | 18.3 | |
| 3 | 26.3 | |
| 4 | 18.6 | 34.88 |
| 5 | 36 | 36.71 |
| 6 | 81.3 | x |
| 7 | 35.7 | 39.71 |
| 8 | 26.4 | 40.86 |
| 9 | 31.5 | 42.14 |
| 10 | 29.6 | |
| 11 | 45.3 | |
| 12 | y |
Consider the time series data presented in the table:
| \text{Time period} | \text{Raw data} | \text{4 point centred}\\\text{moving average} | \text{6 point centred}\\\text{moving average} |
|---|---|---|---|
| 1 | 89 | ||
| 2 | 102.5 | ||
| 3 | 93.5 | 98.09 | |
| 4 | 111 | a | b |
| 5 | 81.7 | 94 | 94.77 |
| 6 | 92.6 | 92.09 | 93.08 |
| 7 | 87.9 | 89.96 | 88.96 |
| 8 | c | 87.56 | 85.93 |
| 9 | 74.4 | 84.54 | 85.79 |
| 10 | 80.7 | 82.48 | |
| 11 | 75.6 | ||
| 12 | d |
Calculate the values of a and b correct to two decimal places.
Calculate the values of c and d correct to one decimal place.
Which centred moving average best smooths the data?
Consider the time series data presented in the table:
| \text{Time period} | \text{Raw data} | \text{3 point centred}\\\text{moving average} | \text{4 point centred}\\\text{moving average} |
|---|---|---|---|
| 1 | 11 | ||
| 2 | 8.4 | 19.1 | |
| 3 | 37.9 | 20.87 | 19.14 |
| 4 | 16.3 | a | 23.95 |
| 5 | 16.9 | 24.73 | 25.89 |
| 6 | 41 | 26.23 | 24.09 |
| 7 | 20.8 | 26.93 | b |
| 8 | c | 27.87 | 28.68 |
| 9 | 43.8 | 28 | 25.81 |
| 10 | 21.2 | 27.57 | 28.65 |
| 11 | 17.7 | 27.9 | |
| 12 | d |
Calculate the value of a in the table. Give your answer to two decimal places.
Find the value of b. Give your answer to two decimal places.
Calculate the values of c and d correct to one decimal place.
Which moving average best smooths the data?
Jack the accountant records the following data regarding company turnover from 2002 to 2016 into a spreadsheet program. He wishes to smooth the data to investigate any underlying trend in the data so he uses the spreadsheet program to calculate moving averages:
Write a spreadsheet formula that Jack could type into cell \text{C3} to calculate the 3 point moving average for the data set.
Write a spreadsheet formula that Jack could type into cell \text{D4} to calculate the 5 point moving average for the data set.
Write a spreadsheet formula that Jack could type into cell \text{E4} to calculate the 4 point centred moving average for the data set.
Which moving average smooths the data the best?
A supermarket records plastic bag use and decides to use a 4 point centred moving average to smooth the data in order to make predictions.
The data is shown in the following spreadsheet:
Write a spreadsheet formula the supermarket staff could type into cell \text{C4} to calculate the 4CMA.
Justin weighs himself every 4 months and plots his weight on the graph below:
What type of moving average should Justin use if he wishes to smooth the data in order to make predictions and have the moving average values plotted at each month and not between months?
Justin enters the following incorrect formula into cell \text{D3} in his spreadsheet in order to calculate a 4 point centred moving average:
Write the correct formula for \text{D3}.
Calculate the correct result for the 4CMA that will be displayed in cell \text{D3}. Give your answer to one decimal place.
Paul records the average hours he works per week each month and records the data below:
What type of moving average should Paul use if he wishes to smooth the data and have the moving average figures plotted for each month and not between each month?
Paul enters the following formula into cell \text{C33} in his spreadsheet in order to calculate a 4 point centred moving average:
Write the correct formula and state which cell the formula should be typed into.
Hence, calculate the correct value for the 4CMA. Round your answer to one decimal place.
The graph shows the number of visitors to Kings' Park. Data is recorded every second month from January 2015 to November 2019:
What type of moving average should King’s Park administrators use if they wish to smooth the data in order to make predictions using a linear regression model?
The administrators set up a spreadsheet and enter the following formula into cell \text{E4} to calculate a 6 point centred moving average:
Write the correct formula for this cell.
Calculate the value that will be displayed by the correct formula in cell \text{E4}. Round your answer to two decimal places.