Doaba Sweets: Two Outlets, Two Averages, One Valuation
Doaba Sweets runs two retail outlets in Ludhiana. The owner, Kamal, is negotiating the sale of one outlet and has based his asking price on average daily sales. He has twelve randomly chosen days of recorded daily sales in rupees from each outlet. Outlet A (Model Town): 8,200; 7,900; 8,500; 8,100; 7,800; 8,300; 8,000; 8,400; 7,700; 8,600; 8,200; 48,000. Outlet B (Sarabha Nagar): 9,000; 8,800; 9,200; 8,700; 9,100; 8,900; 9,300; 8,600; 9,000; 8,800; 9,200; 8,700. The ₹48,000 day at Outlet A was a single wedding order for 400 sweet boxes; such orders arise three or four times a year and cannot be predicted in advance. The prospective buyer has looked only at the two means and argues that Outlet A is the stronger business and therefore Outlet B should be priced lower. Kamal's accountant disagrees with him.
1. Calculate the mean and median daily sales of both outlets and explain why the two measures tell different stories.
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Outlet A
Sum = 8,200 + 7,900 + 8,500 + 8,100 + 7,800 + 8,300 + 8,000 + 8,400 + 7,700 + 8,600 + 8,200 + 48,000 = ₹1,37,700.
Mean = 1,37,700 ÷ 12 = ₹11,475.
Arranged in order: 7,700; 7,800; 7,900; 8,000; 8,100; 8,200; 8,200; 8,300; 8,400; 8,500; 8,600; 48,000. The 6th and 7th values are both 8,200, so Median = ₹8,200.
Outlet B
Sum = 9,000 + 8,800 + 9,200 + 8,700 + 9,100 + 8,900 + 9,300 + 8,600 + 9,000 + 8,800 + 9,200 + 8,700 = ₹1,07,300.
Mean = 1,07,300 ÷ 12 = ₹8,941.67.
Arranged in order: 8,600; 8,700; 8,700; 8,800; 8,800; 8,900; 9,000; 9,000; 9,100; 9,200; 9,200; 9,300. Median = (8,900 + 9,000)/2 = ₹8,950.
Why they differ: the mean uses every value, so the single ₹48,000 wedding order pulls Outlet A's mean above every ordinary day it ever has. The median is positional; it ignores the size of the extreme value and sits on the eighth-ranked day. Confirm the distortion: dropping the wedding day, Outlet A's mean over the remaining eleven days is 89,700 ÷ 11 = ₹8,154.55, well below Outlet B. The range tells the same story - Outlet A spans ₹40,300 against Outlet B's ₹700, so A is also far more volatile.
2. Whose argument is stronger, the buyer's or the accountant's? Which measure should Kamal use for valuing a typical day's trading and which for forecasting annual revenue?
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The accountant is right about the buyer's comparison, but wrong if he claims Outlet A is simply weaker.
For a typical day, use the median. The median of Outlet A (₹8,200) is below the median of Outlet B (₹8,950). On an ordinary day Outlet B sells about ₹750 more. The buyer is comparing means inflated by an event that is not part of routine trading, so his conclusion is unsound.
For annual revenue, neither mean from this sample should be used directly. The wedding order is real revenue and recurs three or four times a year, so it cannot simply be deleted. Build the estimate from two components:
- Ordinary days: Outlet A ≈ 8,200 × 365 = ₹29,93,000; Outlet B ≈ 8,950 × 365 = ₹32,66,750.
- Wedding-type surplus at A: each event adds roughly 48,000 − 8,200 = ₹39,800 above an ordinary day. At 3.5 events a year that is about ₹1,39,300.
- Estimated annual sales: Outlet A ≈ ₹31,32,300; Outlet B ≈ ₹32,66,750.
So Outlet B is ahead even after crediting A with its bulk orders, and it is ahead with far less uncertainty (range ₹700 against ₹40,300). That supports a higher valuation for Outlet B, not a lower one, and it reverses the buyer's claim.
The lesson: the mean is the right measure for totals and for further statistical work, but it is not robust when the distribution is skewed by one extreme observation. Whenever an average is used to price something, ask what single value could move it and whether that value is repeatable.
3. What further information would you demand before advising Kamal to accept or reject the buyer's price?
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The twelve-day sample answers only the question 'what is a normal day's sale'. A valuation needs profitability, risk and sustainability, so ask for:
- Twelve months of daily sales records, not twelve days. This removes sampling error and shows whether the ₹48,000 day was typical of the year or the only one.
- Seasonality. Sweet sales peak at Diwali, Rakhi and the wedding season. If the sample was drawn in a lean month, both medians understate the year.
- Gross margin by product line, not just turnover. Wedding-box orders are usually quoted at a thin margin. A ₹48,000 order may contribute less profit than three ordinary days of retail counter sales, which would weaken Outlet A's revenue advantage further and change the ranking entirely.
- Costs traceable to each outlet - rent, staff, electricity, wastage of perishable stock. A high-turnover outlet with high rent and heavy wastage can be worth less than a modest, steady one.
- Capacity and effort constraints. Can Outlet A's kitchen actually service four wedding orders a month, and who does the extra work? If the owner himself works nights for those orders, the apparent profit is partly unpaid wages.
- Trend and competition. Two or three years of figures show whether sales are rising or falling, and any new competitor nearby.
- The basis of the asking price. Is it a multiple of annual sales, of annual profit, or of net assets including fittings and the lease? The measure chosen must match the statistic used.
Advice: reject the buyer's reasoning now, but do not fix a price until a full year's figures and outlet-wise margins are in hand. A median of a proper sample, multiplied by margins, is the defensible basis.