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5.06 Exam style questions (calculator assumed )

Interactive practice questions

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.

Performance day Performance number ($N$N) Attendance numbers 4CMA
Week $1$1 Fri $1$1 $1087$1087  
Sat (matinée) $2$2 $844$844  
Sat (evening) $3$3 $1731$1731 $1231.0$1231.0
Sun $4$4 $1232$1232 $B$B
Week $2$2 Fri $5$5 $1003$1003 $1192.0$1192.0
Sat (matinée) $6$6 $802$802 $1172.8$1172.8
Sat (evening) $7$7 $1731$1731 $1147.3$1147.3
Sun $8$8 $1078$1078 $1133.6$1133.6
Week $3$3 Fri $9$9 $953$953 $1121.1$1121.1
Sat (matinée) $10$10 $743$743 $1100.5$1100.5
Sat (evening) $11$11 $1690$1690 $1078.3$1078.3
Sun $12$12 $954$954 $1059.9$1059.9
Week $4$4 Fri $13$13 $899$899 $1034.5$1034.5
Sat (matinée) $14$14 $650$650 $1009.6$1009.6
Sat (evening) $15$15 $1580$1580  
Sun $16$16 $A$A  
a

What is the break even attendance figure for the ballet company?

Round your answer to the nearest whole number.

b

Find the value $A$A.

Round your answer to the nearest whole number.

c

Find the value $B$B.

Round your answer to one decimal place.

Medium
7min

A ballet company performed $4$4 times a week for four weeks at the Perth Concert Hall. The table below shows the attendance figures for Week $2$2.

Easy
1min

A ballet company performed $4$4 times a week for four weeks at the Perth Concert Hall. Information about the attendance numbers at the ballet is given in the table below.

Easy
1min

A ballet company performed $4$4 times a week for four weeks at the Perth Concert Hall. The attendance data and the moving average data for the four weeks have been drawn below.

Easy
< 1min
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Outcomes

4.1.2

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

4.1.3

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

4.1.4

calculate seasonal indices by using the average percentage method

4.1.5

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

4.1.6

fit a least-squares line to model long-term trends in time series data

4.1.7

predict from regression lines, making seasonal adjustments for periodic data

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