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5.06 Further applications

Interactive practice questions

A hairdressing salon at a local shopping centre records the number of customers per day and the results are shown in the graph below.

Comment on the trend and seasonality of the data. Select all that apply.

There is a downwards trend over time.

A

The trend is that the numbers stay stable.

B

There is an upwards trend over time.

C

There are $4$4 seasons in a cycle.

D

There are $5$5 seasons in a cycle.

E
Easy
< 1min

The table below shows some time series data where $t$t represents time.

Easy
1min

A cat boarding kennel records its number of boarders every $4$4 months (tri-annually) ending at January, May and September.

Easy
< 1min

A ballet company performed $4$4 times a week for four weeks at the Perth Concert Hall which is able to seat $1731$1731 patrons. To break even the attendance must be more than $60%$60% of maximum capacity. The attendance at the daily performances are shown in the table below.

Medium
7min
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Outcomes

3.2.1.2

describe time series plots by identifying features such as trend (long-term direction), seasonality (systematic, calendar-related movements) and irregular fluctuations (unsystematic, short-term fluctuations), and recognise when there are outliers, e.g. one-off unanticipated events

3.2.2.1

smooth time series data by using a simple moving average, including the use of spreadsheets to implement this process

3.2.2.2

calculate seasonal indices by using the average percentage method

3.2.2.3

deseasonalise a time series by using a seasonal index, including the use of spreadsheets to implement this process

3.2.2.4

fit a least-squares line to model long-term trends in time series data, using appropriate technology

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