Canteen pricing from a spending survey
A school in Butwal surveys 40 students about daily canteen spending. The responses are grouped:
| Daily spending (NPR) | Number of students | | 0–50 | 4 | | 50–100 | 8 | | 100–150 | 14 | | 150–200 | 9 | | 200–250 | 5 |
The canteen plans a fixed meal combo. It wants the combo price to be affordable to at least 60% of students, and it also wants to estimate the probability that a randomly chosen student spends NPR 150 or more. The manager suggests using the mean spending as the price because the average is fair. A parent argues the median is better because a few high spenders pull the mean up. The canteen also has a cost of NPR 70 per combo. It asks for the median class and median, the mean, the probability of spending at least 150, and a recommendation.
1. Find the median class, the median and the mean of the spending data.
Read the worked answer
Total students N = 40, so the median position is N/2 = 20.
Cumulative frequencies: 4, 12, 26, 35, 40. The 20th student lies in 100–150, so that is the median class.
Median = L + [(N/2 − cf) ÷ f] × h
= 100 + [(20 − 12) ÷ 14] × 50
= 100 + 28.57 = NPR 128.57.
Mean = [4(25) + 8(75) + 14(125) + 9(175) + 5(225)] ÷ 40
= 5,150 ÷ 40 = NPR 128.75.
The mean is slightly higher because the top class pulls it up.
2. Estimate the probability that a randomly chosen student spends NPR 150 or more. What price is affordable to at least 60% of students?
Read the worked answer
Students spending at least 150 = 9 + 5 = 14.
Empirical probability = 14/40 = 0.35, or 35%.
For at least 60% affordability, the price must be at the 40th percentile, not the median. 40% of 40 = 16. The 16th student lies in 100–150, where the cumulative frequency before the class is 12.
Price = 100 + [(16 − 12) ÷ 14] × 50
= 100 + 14.29 = NPR 114.29.
Rounding down to a whole rupee gives NPR 114.
3. Evaluate the manager's and the parent's suggestions. What price should the canteen set, and what margin does it make?
Read the worked answer
At the mean NPR 128.75 or the median NPR 128.57, only about half the students spend at least that amount. Neither meets the 60% affordability rule. The mean is pulled up by high spenders; the median is still only the 50th percentile.
Under the stated uniform-within-class assumption, the 40th percentile is about NPR 114.29. So NPR 114 is the highest whole-rupee price that keeps 60% affordability.
At cost NPR 70, margin = 114 − 70 = NPR 44 per combo.
Recommendation: set the combo at NPR 114 or lower. Use percentile/median thinking for affordability and the mean for total revenue forecasting, not as a fairness price by itself.