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VCE 12 General 2023

4.04 Seasonal indices

Interactive practice questions

From the beginning of 2016, the number of new houses built in the suburb of Woodford was recorded and figures are released every four months.

The following table contains the data from the beginning of 2016 to the end of 2019:

Time Period

Houses built

Percentage of yearly mean

April 2016 $6$6 $60%$60%
August 2016 $21$21 $x$x
December 2016 $3$3 $30%$30%
April 2017 $11$11 $y$y
August 2017 $24$24 $180%$180%
December 2017 $5$5 $37.5%$37.5%
April 2018 $15$15 $84.91%$84.91%
August 2018 $25$25 $141.51%$141.51%
December 2018 $13$13 $z$z
April 2019 $15$15 $77.59%$77.59%
August 2019 $28$28 $144.83%$144.83%
December 2019 $15$15 $77.59%$77.59%
a

For 2016, 2017 and 2018, calculate the mean number of houses built in each time period.

Give your answers to two decimal places.

Year 2016 2017 2018
Mean $\editable{}$ $\editable{}$ $\editable{}$
b

Use your answers from part (a) to calculate the value of $x$x.

Give your answer to two decimal places.

c

Use your answers from part (a) to calculate the value of $y$y.

Give your answer to two decimal places.

d

Use your answers from part (a) to calculate the value of $z$z.

Give your answer to two decimal places.

Easy
6min

The local police station records the number of speeding fines issued each quarter.

The table alongside has the data for each quarter from 2016 to 2018.

Easy
4min

A local grocery store records the number of lemons sold in the first quarters of 2016, 2017, 2018 and 2019.

The table shown has the data for each first quarter up to 2019.

Easy
4min

A local cafe stays open for $5$5 days a week in the city, and records how many cappuccinos they sell on Friday, Saturday and Sunday for four weeks.

The table alongside has the data for the four weeks.

Easy
14min
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Outcomes

U3.AoS1.28

identify key qualitative features of a time series plot including trend (using smoothing if necessary), seasonality, irregular fluctuations and outliers, and interpret these in the context of the data

U3.AoS1.29

calculate, interpret and apply seasonal indices

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