Post by: Yendall on September 30, 2012, 10:43:03 am
Here is the question:
Summer = 1.11
Autumn = 0.78
Winter = 0.49
Spring = 1.62
Charles sells 23 bouquets of flowers during summer and wants to improve on his sales during the next season, autumn. Using the seasonal indices given above, the minimum number of bouquets that Charles must sell in autumn to outperform his sales in summer is:
Autumn = 0.78
Winter = 0.49
Spring = 1.62
Charles sells 23 bouquets of flowers during summer and wants to improve on his sales during the next season, autumn. Using the seasonal indices given above, the minimum number of bouquets that Charles must sell in autumn to outperform his sales in summer is:
How I attempted this was using the deseasonalise formula
By solving for how many bouquets were sold in Summer, in relation to the seasonal index of Autumn:
The answer was 17 when rounded, which would work here because you can't have 0.94 of a flower, but the proper deseasonlised value is 16.16. Similarly, it needs to be rounded up as he cannot sell a portion of bouquet.
How would I solve this to get 16.16?
Post by: BubbleWrapMan on September 30, 2012, 10:57:07 am
Post by: Yendall on September 30, 2012, 10:58:21 am
He sold 23/1.11 = 20.72 bouquets in summer (de-seasonalised), you then multiply it 20.72 by 0.78 to get 16.16 which the relative seasonal value for autumn. To improve his sales he has to sell at least 17 (16 would be less).Okay thank you! so you always deseasonalise the initial data set before determining the next?
Post by: BubbleWrapMan on September 30, 2012, 11:07:06 am
Post by: Yendall on September 30, 2012, 11:14:13 am
The idea behind de-seasonalising data is so that you can compare between seasons. If you keep that in mind it makes most of these problems much easier. Also, it wouldn't make sense to use the seasonal index for autumn but not for summer.Okay cool, that makes sense :)
"Deseasonlising = removing the seasonal component from the data"
Is this pretty much removing the average and dealing with raw data in replacement?
Post by: BubbleWrapMan on September 30, 2012, 11:55:27 am
To use an example where we don't know the seasonal indices, think about Christmas trees. If a local business sold 10 trees in June, that would be an extremely high amount (you wouldn't really expect anyone to buy them), but if they sold 10 trees in December that would be considered extremely poor.
One generally has an idea of the fact that sales vary with seasons, and seasonal indices simply give us a quantitative method for analysing these trends instead of just saying "we done good, considering it's winter." :P
Post by: Yendall on September 30, 2012, 12:09:10 pm
Yeah, it basically just accounts for variation in sales or other things due to seasonal trends and allows you to compare between them. For example if Charles sold 111 bouquets in summer and 78 in autumn that would pretty much be what you'd expect as a relative amount between the two seasons, but if he sold 100 in summer and 100 in autumn that would be considered a relatively bad figure for summer but a relatively good figure for autumn, even though he sold the same amount in both seasons.Yeah exactly, I understand that :) The seasonal indices are sort of an amount to show whether they have performed poorly or well. Say they did sell 10 trees in December, a reasonable Seasonal Index might be 0.50 or something, yes? whereas in June it would be around 1.20 to show that they've sold above the average for the season, at that point in time?
To use an example where we don't know the seasonal indices, think about Christmas trees. If a local business sold 10 trees in June, that would be an extremely high amount (you wouldn't really expect anyone to buy them), but if they sold 10 trees in December that would be considered extremely poor.
One generally has an idea of the fact that sales vary with seasons, and seasonal indices simply give us a quantitative method for analysing these trends instead of just saying "we done good, considering it's winter." :P
Post by: Stick on September 30, 2012, 12:12:56 pm
This is a great question which I have never come across before. I'm putting this in my bound reference. :P
Post by: BubbleWrapMan on September 30, 2012, 12:29:59 pm
Yeah exactly, I understand that :) The seasonal indices are sort of an amount to show whether they have performed poorly or well. Say they did sell 10 trees in December, a reasonable Seasonal Index might be 0.50 or something, yes? whereas in June it would be around 1.20 to show that they've sold above the average for the season, at that point in time?No, it would be more like the seasonal index for June for past years would be something low like 0.5, so when you sell 10 trees in June it's equivalent to selling 20 as a de-seasonalised value, or 20*1.20 = 24 trees in December. In general you can't tell what the seasonal index for a future season will be, you just use past data and predict the amount you should expect to sell.
If you sell 10 trees in December its de-seasonalised value is 10/1.20 = 8.33, and so 10 trees in December is equivalent to 8.33*0.5 = 4.17 trees in June.
If you look at your example in the first post, the seasonal index for spring was highest, which means Charles makes more than the yearly average amount of sales in spring, which is what you'd expect.
Post by: Yendall on September 30, 2012, 12:31:32 pm
Okay awesome :) if you were to evaluate that you could say he makes more sales in Spring because flowers are in blossom at that time of year etc.Yeah exactly, I understand that :) The seasonal indices are sort of an amount to show whether they have performed poorly or well. Say they did sell 10 trees in December, a reasonable Seasonal Index might be 0.50 or something, yes? whereas in June it would be around 1.20 to show that they've sold above the average for the season, at that point in time?No, it would be more like the seasonal index for June for past years would be something low like 0.5, so when you sell 10 trees in June it's equivalent to selling 20 as a de-seasonalised value, or 20*1.20 = 24 trees in December. In general you can't tell what the seasonal index for a future season will be, you just use past data and predict the amount you should expect to sell.
If you sell 10 trees in December its de-seasonalised value is 10/1.20 = 8.33, and so 10 trees in December is equivalent to 8.33*0.5 = 4.17 trees in June.
If you look at your example in the first post, the seasonal index for spring was highest, which means Charles makes more than the yearly average amount of sales in spring, which is what you'd expect.