Canteen Sales: Typical Day or Total Budget?
The government higher secondary school in a taluk town runs a canteen during the lunch break. For 11 consecutive school days the canteen’s daily sales (in ₹) were: 2,450; 2,510; 2,380; 2,600; 2,470; 2,550; 2,490; 2,430; 9,900; 2,520; 2,410. The ninth day was the annual sports meet, when visiting parents and alumni bought food throughout the day. The canteen manager must submit two different figures: an estimate of a typical day for normal stock planning, and a total purchasing budget for a 20-day working month. A parent–teacher association member says to use the average of all 11 days; another says to drop the sports-meet day entirely. The manager cannot stock according to a figure that is too high or too low, because unsold perishables are wasted and stock-outs lose sales. The school also wants to compare this year’s typical sales with last year’s, when no sports meet was held.
1. Calculate the mean and median of the 11 daily sales figures. Which would you report as the typical daily sale, and why?
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Sum = 2,450 + 2,510 + 2,380 + 2,600 + 2,470 + 2,550 + 2,490 + 2,430 + 9,900 + 2,520 + 2,410 = 34,710. Mean = 34,710/11 = ₹3,155.45. Sorted data: 2,380; 2,410; 2,430; 2,450; 2,470; 2,490; 2,510; 2,520; 2,550; 2,600; 9,900. The 6th value is ₹2,490, so median = ₹2,490. The sports-meet day (₹9,900) is a genuine but atypical observation. It pulls the mean upward by about ₹665 relative to the median. For a 'typical' normal day, report the median ₹2,490, or the mean excluding the sports day, ₹2,481; the mean of all 11 days describes a mixed type of day, not an ordinary day.
2. The manager needs a 20-day purchasing budget. What should be used if the 20 days are ordinary days? What if the sports meet is one of those 20 days? Explain the purpose of each figure.
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For ordinary days, use the no-sports-day mean: (34,710 − 9,900)/10 = 2,481, so budget = 20 × 2,481 = ₹49,620. If the sports meet is known to fall within the 20 days, budget 19 ordinary days plus the event: 19 × 2,481 + 9,900 = 47,139 + 9,900 = ₹57,039. Using 20 × 3,155.45 = ₹63,109 assumes the event occurs about twice a month, which is false for an annual event. The median (20 × 2,490 = ₹49,800) is close for an ordinary month but cannot capture the event day's total.
3. Should the sports-meet day be omitted when comparing with last year? Recommend a defensible approach.
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For a like-for-like comparison with last year, compare ordinary days: use the 10-day mean ₹2,481 or the median ₹2,490, and disclose that the sports day is excluded. Do not simply drop it without explanation. A defensible report shows both typical ordinary-day sales and the separate sports-meet sales. If last year had no sports meet, including ₹9,900 would make this year look better for a reason unrelated to normal canteen demand.