For each of the following tables calculate the value of x, y, \text{ and }z:
| \text{Time period} | \text{Data} | \text{3-Point Median} |
|---|---|---|
| 1 | 54 | |
| 2 | 45 | x |
| 3 | 50 | 47 |
| 4 | y | 47 |
| 5 | 42 | 47 |
| 6 | 48 | 48 |
| 7 | 49 | 48 |
| 8 | 43 | z |
| 9 | 48 | 47 |
| 10 | 47 | 47 |
| 11 | 39 | 46 |
| 12 | 46 |
| \text{Time period} | \text{Data} | \text{5-Point Median} |
|---|---|---|
| 1 | 9.2 | |
| 2 | 11 | |
| 3 | 10.7 | x |
| 4 | 9.5 | 10.5 |
| 5 | 9.6 | 10.5 |
| 6 | y | 10.5 |
| 7 | 11.5 | 11.4 |
| 8 | 11.5 | 11.4 |
| 9 | 11.4 | 11.4 |
| 10 | 10.9 | z |
| 11 | 10.5 | |
| 12 | 12.2 |
| \text{Time period} | \text{Data} | \text{3-Point Median} |
|---|---|---|
| 1 | 534 | |
| 2 | 346 | x |
| 3 | 213 | 346 |
| 4 | y | 678 |
| 5 | 874 | 753 |
| 6 | 753 | 753 |
| 7 | 679 | 679 |
| 8 | 186 | z |
| 9 | 348 | 348 |
| 10 | 547 | 369 |
| 11 | 369 | 486 |
| 12 | 486 |
| \text{Time period} | \text{Data} | \text{5-Point Median} |
|---|---|---|
| 1 | 19.1 | |
| 2 | 10.5 | |
| 3 | 18.2 | x |
| 4 | 12.4 | 14.1 |
| 5 | 29.8 | 14.1 |
| 6 | y | 14.1 |
| 7 | 7 | 14.1 |
| 8 | 14.2 | 14.1 |
| 9 | 6.9 | 8.7 |
| 10 | 27.6 | z |
| 11 | 8.7 | |
| 12 | 0.4 |
The Smith family review the money they spent on groceries each month in 2019. The results are given in the table:
Calculate the values of a, b, \text{ and } c.
| \text{Time period} | \text{Data} | \text{3-Point Median} |
|---|---|---|
| \text{Jan} | 986 | |
| \text{Feb} | 1004 | 1004 |
| \text{Mar} | 1051 | a |
| \text{Apr} | 1010 | 1010 |
| \text{May} | 978 | 1006 |
| \text{Jun} | b | 1006 |
| \text{Jul} | 1015 | 1015 |
| \text{Aug} | 1043 | 1043 |
| \text{Sep} | 1071 | c |
| \text{Oct} | 1028 | 1053 |
| \text{Nov} | 1053 | 1053 |
| \text{Dec} | 1092 |
The Reid family review the money they’ve spent on household bills. The results are given in the table:
Calculate the values of a, b, \text{ and } c.
| \text{Time period} | \text{Data} | \text{3-Point Median} |
|---|---|---|
| \text{Jan} | 1017 | |
| \text{Feb} | 975 | 1017 |
| \text{Mar} | 1022 | a |
| \text{Apr} | 1006 | 1021 |
| \text{May} | 1021 | 1021 |
| \text{Jun} | b | 1041 |
| \text{Jul} | 1042 | 1041 |
| \text{Aug} | 1005 | 1042 |
| \text{Sep} | 1052 | c |
| \text{Oct} | 1061 | 1052 |
| \text{Nov} | 1034 | 1061 |
| \text{Dec} | 1064 |
The following time series graph shows the temperature (\degree \text{C}) recorded for the 29 days of February in a particular leap year:
Calculate the 5-median smoothed temperature for:
Day 12
Day 14
The following time series graph shows the number of days it rained each month in a year:
Calculate the 5-median smoothed number of days for the following months:
April
July
October
The following time series plot shows the number of passengers who flew with an airline each month from 1955 to 1958:
The dot above 1955 corresponds to the number of passengers in January 1955. Which value is the five-median smoothed number of passengers for August 1955 closest to?
For each of the following Time Series graphs, calculate, plot and connect the six 3-point moving medians to smooth the data:
For each of the following Time Series graphs, calculate, plot and connect the six 5-point moving medians to smooth the data:
The time series plot shows the minimum rainfall recorded at the weather station each month plotted against the month number (January = 1).
Rainfall is recorded in millimetres. The data was collected over a period of one year.
Calculate, plot and connect 8 additional points to create a 5-point moving median graph.
The time series plot shows the average rainfall, in millimetres, recorded at the weather station over twelve weeks:
Calculate, plot and connect 8 additional points to create a 5-point moving median graph.