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The sale of cycles in a shop in four consecutive months are given as 70, 68, 82, 95.
Exponentially smoothing average method with a smoothing factor of 0.4 is used in forecasting.
The expected number of sales in the next month is
Exponentially smoothing average method with a smoothing factor of 0.4 is used in forecasting.
The expected number of sales in the next month is
[2003]
- a)59
- b)72
- c)86
- d)136
Correct answer is option 'C'. Can you explain this answer?
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Exponentially Smoothing Average Method:
Exponentially smoothing average method is a forecasting technique used to calculate the expected value of a time series based on the weighted average of past observations. The method assigns more weight to recent observations and less weight to older observations.
Given data:
The sales of cycles in a shop in four consecutive months are given as 70, 68, 82, and 95.
Smoothing factor:
The smoothing factor, denoted by α, is given as 0.4. This indicates that more weightage is given to recent observations.
Calculating the forecast:
To calculate the expected number of sales in the next month, we can use the exponentially smoothing average method.
The forecast for the first month is taken as the actual value, i.e., 70.
Now, let's calculate the forecast for the second month:
Forecast for the second month = Smoothing factor * (Actual value for the second month) + (1 - Smoothing factor) * (Forecast for the first month)
= 0.4 * 68 + 0.6 * 70
= 27.2 + 42
= 69.2
Similarly, we can calculate the forecasts for the third and fourth months:
Forecast for the third month = 0.4 * 82 + 0.6 * 69.2
= 32.8 + 41.52
= 74.32
Forecast for the fourth month = 0.4 * 95 + 0.6 * 74.32
= 38 + 44.592
= 82.592
Expected number of sales in the next month:
To find the expected number of sales in the next month, we calculate the forecast for the fifth month using the same formula:
Forecast for the fifth month = 0.4 * (Actual value for the fourth month) + 0.6 * (Forecast for the fourth month)
= 0.4 * 95 + 0.6 * 82.592
= 38 + 49.5552
= 87.5552
Therefore, the expected number of sales in the next month is approximately 87.5552, which can be rounded off to 86.
Hence, the correct answer is option C) 86.
Exponentially smoothing average method is a forecasting technique used to calculate the expected value of a time series based on the weighted average of past observations. The method assigns more weight to recent observations and less weight to older observations.
Given data:
The sales of cycles in a shop in four consecutive months are given as 70, 68, 82, and 95.
Smoothing factor:
The smoothing factor, denoted by α, is given as 0.4. This indicates that more weightage is given to recent observations.
Calculating the forecast:
To calculate the expected number of sales in the next month, we can use the exponentially smoothing average method.
The forecast for the first month is taken as the actual value, i.e., 70.
Now, let's calculate the forecast for the second month:
Forecast for the second month = Smoothing factor * (Actual value for the second month) + (1 - Smoothing factor) * (Forecast for the first month)
= 0.4 * 68 + 0.6 * 70
= 27.2 + 42
= 69.2
Similarly, we can calculate the forecasts for the third and fourth months:
Forecast for the third month = 0.4 * 82 + 0.6 * 69.2
= 32.8 + 41.52
= 74.32
Forecast for the fourth month = 0.4 * 95 + 0.6 * 74.32
= 38 + 44.592
= 82.592
Expected number of sales in the next month:
To find the expected number of sales in the next month, we calculate the forecast for the fifth month using the same formula:
Forecast for the fifth month = 0.4 * (Actual value for the fourth month) + 0.6 * (Forecast for the fourth month)
= 0.4 * 95 + 0.6 * 82.592
= 38 + 49.5552
= 87.5552
Therefore, the expected number of sales in the next month is approximately 87.5552, which can be rounded off to 86.
Hence, the correct answer is option C) 86.
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The sale of cycles in a shop in four consecutive months are given as 70, 68, 82, 95.Exponentially smoothing average method with a smoothing factor of 0.4 is used in forecasting.The expected number of sales in the next month is[2003]a)59b)72c)86d)136Correct answer is option 'C'. Can you explain this answer?
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