SCSA Mathematics Applications Time series analysis

This is the raw data value for Day 4, not the calculated moving average.

This value is incorrect; the average of the second window of data points (10, 18, and 32) is 20, not 25.

This is the raw data value for Day 3, not the calculated moving average.

Incorrect. A 25% reduction would mean multiplying the actual sales by 0.75, which does not match the required deseasonalizing factor of $1/1.75 \approx 0.57$.

Incorrect. This is the percentage that the deseasonalized sales represent of the actual sales ($1/1.75 \approx 57\%$), rather than the percentage by which the actual sales must be reduced.

Incorrect. While a seasonal index of 1.75 means sales are 75% above the seasonal average, reversing this increase requires dividing by 1.75, not subtracting 75%.

This is incorrect. The sum of the temperatures from Wednesday to Sunday is $127.0$, which results in an average of $25.4$, not $25.5$.

This is the actual temperature recorded on Friday ($25.6^\circ\text{C}$), rather than the calculated 5-point moving average.

This value is incorrect. It is significantly higher than the actual average of the temperatures from Wednesday to Sunday.

While the value for $y$ (0.8) is correct, the value for $x$ is incorrect. The average quarterly sales is 160 (calculated as $160/1.0$), so $x$ should be $160 \times 0.95 = 152$.

Both values are incorrect. The sum of quarterly indices must equal 4, making $y=0.8$, and the sales value $x$ is calculated by multiplying the average sales (160) by the index (0.95).

The value for $x$ (152) is correct, but $y$ is incorrect. The sum of the indices must equal 4, not the partial sum of the other indices (3.2).

This assumes the seasonal index follows a linear pattern (0.6, 0.8, 1.0, 1.2) and divides sales by 1.2. However, seasonal indices must sum to the number of periods (4), making the correct Q4 index 1.6.

This result likely comes from estimating the index incorrectly as 1.2 (based on a pattern) and multiplying it by the sales, rather than dividing by the correct index.

This is the result of multiplying the actual sales by the seasonal index ($7200 \times 1.6$). To deseasonalize data (find seasonally adjusted sales), you must divide the actual sales by the seasonal index.

This value represents the centered moving average for June (calculated as $\frac{89 + 65 + 53}{3} = 69$), rather than May.

This result comes from using a trailing moving average (March, April, May: $\frac{68 + 65 + 89}{3} = 74$), but the problem context establishes that a centered moving average is used.

This is the actual number of books sold in May, not the 3-point moving average.

Incorrect. This is the result of calculating $1 / 1.65$, which would correspond to a 65% increase rather than a 35% increase.

Incorrect. This incorrectly assumes the seasonal index is found by simply subtracting the percentage increase from 1 ($1 - 0.35 = 0.65$).

Incorrect. This is a miscalculation. The correct seasonal index is found by solving $1.35 = 1 / \text{Seasonal Index}$.

Incorrect. This value would be the seasonal index if the actual number of visitors was increased by about 30% ($1 / 1.30 \approx 0.77$), not 35%.