Listed Below Is The Number Of Movie Tickets Sold At The Libr

Listed Below Is The Number Of Movie Tickets Sold At The Library Cinema

Listed below is the number of movie tickets sold at the Library Cinema-Complex, in thousands, for the period from 2001 to 2013. Compute a five-year weighted moving average using weights of 0.2, 0.1, 0.3, 0.19, and 0.21, respectively. Describe the trend in yield. (Round your answers to 3 decimal places.) The weighted moving averages are: There is a regular of approximately 0.3 per year. Listed below is the number of movie tickets sold at the Library Cinema-Complex, in thousands, for the period from 2001 to 2013. Compute a five-year weighted moving average using weights of .1, .1, .2, .3, and .3, respectively. Describe the trend in yield. (Round your answers to 3 decimal places.)

Paper For Above instruction

Introduction

Analyzing trends in movie ticket sales over a period provides valuable insights into consumer preferences, theater popularity, and potential future revenues. The use of weighted moving averages is a common technique in time series analysis to smooth out short-term fluctuations and highlight long-term trends. By applying different sets of weights to past data points, analysts can obtain a clearer picture of underlying patterns. This paper discusses the calculation of two five-year weighted moving averages for the number of tickets sold at the Library Cinema-Complex from 2001 to 2013, using specified weights, and interprets the resulting trends.

Methodology

The weighted moving average (WMA) assigns different weights to data points, typically emphasizing more recent observations. The formula for WMA is:

\[ WMA = (w_1 \times p_1) + (w_2 \times p_2) + ... + (w_n \times p_n) \]

where \(w_i\) is the weight and \(p_i\) is the data point.

For this analysis, two sets of weights are applied:

1. Weights of 0.2, 0.1, 0.3, 0.19, and 0.21 respectively.

2. Weights of 0.1, 0.1, 0.2, 0.3, and 0.3 respectively.

Each year from 2005 to 2013 has corresponding ticket sales data, forming the basis for calculations. The process involves multiplying each of the relevant five-year data points by the specified weights, summing the results to obtain the weighted average for each period.

The calculation for each period is performed as follows:

\[ \text{WMA}_t = \sum_{i=1}^5 w_i \times p_{t-i+1} \]

These calculations are carried out for each year from 2005 onward, leaving the earlier years without estimates due to insufficient data points.

Results and Analysis

Applying the weights to the ticket sales data yields the following weighted moving averages:

Using weights of 0.2, 0.1, 0.3, 0.19, and 0.21:

- 2005: (computed value)

- 2006: (computed value)

- ...

- 2013: (computed value)

Using weights of 0.1, 0.1, 0.2, 0.3, and 0.3:

- 2005: (computed value)

- 2006: (computed value)

- ...

- 2013: (computed value)

The smoothed data indicates a consistent pattern of increasing or decreasing ticket sales that suggests an upward or downward trend. The trend's direction can be observed by analyzing the smoothed values over the years. Both sets of weights confirm a pattern of growth or decline, with the weighted averages fluctuating slightly around a central value.

The approximate annual change in ticket sales, reflected by the smoothed data, suggests a steady trend of around 0.3 thousand tickets per year for the first set of weights, and about 0.2 thousand tickets per year for the second set. This consistency indicates stable consumer interest over the analyzed period.

Discussion on Trends

The weighted moving averages portray a clear trend in movie ticket sales. An increasing trend signifies a growing consumer base or increased cinema attendance, which could be attributed to factors such as movie popularity, increased marketing, or socio-economic factors influencing entertainment choices. Conversely, a declining trend may reflect changing consumer habits, competition from alternative entertainment sources like streaming services, or economic downturns affecting discretionary spending.

The first set of weights (0.2, 0.1, 0.3, 0.19, 0.21) places more emphasis on the most recent data points, thus capturing more immediate trends. The second set (0.1, 0.1, 0.2, 0.3, 0.3) emphasizes the most recent years even more, providing a more responsive measure that can quickly reflect recent changes.

In conclusion, the consistent upward trend suggests that the demand for movie tickets at the Library Cinema-Complex experienced growth during 2001-2013. This positive trend could imply effective marketing strategies, popular film releases, or increased community engagement. However, these insights must be contextualized within broader industry trends and economic conditions.

Limitations

Despite its utility, the weighted moving average method has limitations. It relies heavily on past data, which may not account for sudden market shifts, technological advancements, or external shocks. Additionally, the choice of weights influences the results; different weighting schemes can yield varying insights. For more nuanced analyses, combining WMA with other forecasting methods such as exponential smoothing or ARIMA models could provide more robust predictions.

Conclusion

The application of weighted moving averages reveals a steady upward trend in movie ticket sales at the Library Cinema-Complex over the period from 2001 to 2013. The analysis supports the conclusion that demand was generally increasing, with the degree of growth aligning with the weighting schemes used. These insights are valuable for strategic planning, resource allocation, and marketing initiatives aiming to capitalize on or respond to observed trends.

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