Question 6
The table shows the number of bookings at a restaurant over seven months.
| Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Bookings | 42 | 38 | 61 | 45 | 47 | 52 | 49 |
Determine the 3-point moving median for month 4.
Not quite. You took the middle value without ordering: month 4’s own value, 45.
That is it. Step through the hints below to see why.
Not quite. You used a 5-point moving mean (months 2 to 6): $\dfrac{38+61+45+47+52}{5}=\dfrac{243}{5}=48.6$.
Not quite. You used the 3-point moving mean: $\dfrac{61+45+47}{3}=\dfrac{153}{3}=51$.
The thick box shows the months the tested option uses.
Choose an option to box the months it uses and see its working.
Months 3 to 5, as listed: 61, 45, 47.
Middle value without ordering: 45.
Months 3 to 5 in order: 45, 47, 61.
Median: 47.
Months 2 to 6, mean:
$$\dfrac{38+61+45+47+52}{5}=\dfrac{243}{5}=48.6$$
Months 3 to 5, mean:
$$\dfrac{61+45+47}{3}=\dfrac{153}{3}=51$$
(A) takes the middle of the list before ordering it, which is just month 4’s own value. Order the three values first.
(B) orders the three months centred on month 4 and takes the middle value, so it is the 3-point moving median.
(C) uses five months and a mean, not three months and a median.
(D) uses the right three months but takes their mean, not their median.
Try the question first. Choose a hint above when you want one.
The window for month 4 is months 3, 4 and 5: 61, 45, 47.
In order: 45, 47, 61, so the median is 47.
A 3-point moving median is the middle value of the three months centred on month 4, once they are in order.
The window for month 4 is months 3, 4 and 5: 61, 45, 47. In order these are 45, 47, 61, so the 3-point moving median is 47.
Only mark this done when you could do it without help. Reading the solution does not count.
A Tangent Tuition mock exam question. It is not a past QCAA question, and Tangent Tuition is not affiliated with the QCAA.
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