Developing a project by conducting a survey and preparing a report helps in understanding how statistical tools and methods are applied to analyze real-world economic problems. These tools are essential for analyzing economic activities such as production, consumption, distribution, banking, insurance, trade, and transport.
This sample project demonstrates how a young entrepreneur can plan and execute a market survey to assess consumer preferences, demand, and expenditure patterns before launching a new brand of toothpaste.
The primary objective is to study consumer tastes, monthly expenditures, brand loyalty, and media influences. A structured questionnaire is designed to collect primary data from a sample of 100 households.
Data collected from 100 households is organized and analyzed using statistical tools. Below are the calculations for monthly family income and monthly expenditure on toothpaste.
Using the step-deviation method to calculate the Mean and Standard Deviation of monthly family income:
| Income Class (Rs) | Midpoint ($x$) | Frequency ($f$) | $d' = \frac{X - 20000}{5000}$ | $fd'$ | $fd'^2$ |
|---|---|---|---|---|---|
| 0 - 10,000 | 5,000 | 20 | -3 | -60 | 180 |
| 10,000 - 20,000 | 15,000 | 40 | -1 | -40 | 40 |
| 20,000 - 30,000 | 25,000 | 30 | 1 | 30 | 30 |
| 30,000 - 40,000 | 35,000 | 10 | 3 | 30 | 90 |
| Total | 100 | -40 | 340 |
Mean Income Calculation:
$$\bar{X} = A + \frac{\sum fd'}{\sum f} \times c$$$$\bar{X} = 20000 + \frac{-40}{100} \times 5000 = 20000 - 2000 = \text{Rs. } 18,000$$Standard Deviation of Income Calculation:
$$\sigma = \sqrt{\frac{\sum fd'^2}{\sum f} - \left(\frac{\sum fd'}{\sum f}\right)^2} \times c$$$$\sigma = \sqrt{\frac{340}{100} - \left(\frac{-40}{100}\right)^2} \times 5000$$$$\sigma = \sqrt{3.40 - 0.16} \times 5000 = 1.8 \times 5000 = \text{Rs. } 9,000$$Using the step-deviation method to calculate the Mean and Standard Deviation of monthly expenditure on toothpaste:
| Expenditure Class (Rs) | Midpoint ($x$) | Frequency ($f$) | $d' = \frac{X - 100}{40}$ | $fd'$ | $fd'^2$ |
|---|---|---|---|---|---|
| 0 - 40 | 20 | 5 | -2 | -10 | 20 |
| 40 - 80 | 60 | 20 | -1 | -20 | 20 |
| 80 - 120 | 100 | 40 | 0 | 0 | 0 |
| 120 - 160 | 140 | 30 | 1 | 30 | 30 |
| 160 - 200 | 180 | 5 | 2 | 10 | 20 |
| Total | 100 | 10 | 90 |
Mean Expenditure Calculation:
$$\bar{X} = A + \frac{\sum fd'}{\sum f} \times c$$$$\bar{X} = 100 + \frac{10}{100} \times 40 = \text{Rs. } 104$$Standard Deviation of Expenditure Calculation:
$$\sigma = \sqrt{\frac{\sum fd'^2}{\sum f} - \left(\frac{\sum fd'}{\sum f}\right)^2} \times c$$$$\sigma = \sqrt{\frac{90}{100} - \left(\frac{10}{100}\right)^2} \times 40$$$$\sigma = \sqrt{0.90 - 0.01} \times 40 = 0.89 \times 40 = \text{Rs. } 35.60$$A summary of essential statistical terms used in project design and data analysis: